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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic variety; rational point; family; fibration; density D. Loughran and A. Smeets , 'Fibrations with few rational points', Preprint, 2015, http://arxiv.org/abs/1511.08027 .
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Siegel modular group; Siegel modular function field; seven generators of \(K_ 3\)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) construction of high-rank elliptic curves; Mordell-Weil group K. Nagao, Construction of high-rank elliptic curves, Kobe J. Math,11 (1994), 211--219.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Jacobian; determinantal variety; curve without automorphisms; automorphism group of the moduli space Kouvidakis, A., and Pantev, T., \textit{The automorphism group of the moduli space of semistable}\textit{vector bundles}, Math. Ann. 302 (1995), no. 2, 225--268.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Fermat curve; finite field; rational point Voloch, José Felipe; Zieve, Michael E., Rational points on some Fermat curves and surfaces over finite fields, Int. J. number theory, 10, 2, 319-325, (2014)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Floer cohomology; mirror symmetry; toric manifold; open-closed Gromov-Witten invariant; Saito's theory of singularities, Landau-Ginzburg model; weakly unobstructed Lagrangian submanifold; potential function; Jacobian ring; Frobenius manifold Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K.: Lagrangian Floer theory and mirror symmetry on compact toric manifolds. Astérisque (376), vi+340 (2016). arXiv:1009.1648
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hasse principle; motivic cohomology; zeta function; higher class field theory
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Chevalley-Weil theorem; integral point; rational point; ramification; Puiseux series Strambi, Yu. B. M.; Surroca, A., Quantitative Chevalley-Weil theorem for curves, Monatshefte für Mathematik, 171, 1-32, (2013)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Nash function; normal variety; real closed field; isoalgebraic space; locally semi-algebraic space; topological Zariski main theorem; Riemann extension theorem
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) supersymmetric gauge theory; conformal field theory; instanton partition function; conformal blocks; Liouville theory conformal field theory; Seiberg-Witten theory; \(SL(2,R)\) connections; Darboux coordinates Teschner, J.; Vartanov, GS, Supersymmetric gauge theories, quantization of \( {\text{\mathcal{M}}}_{flat} \) and conformal field theory, Adv. Theor. Math. Phys., 19, 1, (2015)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) line bundles on arithmetic varieties; height functions; arithmetic intersection theory; Néron-Tate height; Jacobian; intersection pairing
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Cremona group; differential invariant; symmetry; invariant derivation; rational function Bibikov, P.; Malakhov, A., On Lie problem and differential invariants for the subgroup of the plane Cremona group, J. Geom. Phys., 121, 72-82, (2017)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) function field; Carlitz module; shtuka; unit group; class group L. Taelman, ''The Carlitz shtuka,'' J. Number Theory, vol. 131, iss. 3, pp. 410-418, 2011.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) generalized Brauer-Severi variety; projective variety; right ideals; central simple algebra; Grassmann variety; function fields; generic partial splitting fields; Brauer group; index Blanchet, A.: Function fields of generalized Brauer-Severi varieties. Comm. in Algebra19 (1991), 97--118
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) higher-dimensional algebraic varieties; birational geometry; birational classification theory; minimal model program; Mori theory; cohomological vanishing theorems; cohomological nonvanishing theorems; Cartier divisors; morphisms from curves; varieties with many rational curves; rational quotient of a variety; cone theorem; contraction theorem; extremal rays Debarre O., Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, New York 2001.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational parametrization; singularities of an algebraic curve; multiplicity of a point; ordinary and non-ordinary singularities; T-function; fiber function
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) germ of real holomorphic function; index of a singular point of a gradient vector field; complex conjugation; homology groups of Milnor fibres S.M. Gusein-Zade, ''The index of a singular point of a gradient vector field,''Funct. Anal. Appl.,18, 6--10 (1984).
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Galois group; elliptic curve; hyperelliptic curve; Jacobian variety; Tate module Yelton, J, Images of \(2\)-adic representations associated to hyperelliptic Jacobians, J. Number Theory, 151, 7-17, (2015)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) discriminant conjecture for elliptic curves; function field; Frey curves; Weil curves Szpiro, L., Discriminant et conducteur des courbes elliptiques, Séminaire sur les Pinceaux de Courbes Elliptiques, Paris, 1988, Astérisque, 183, 7-18, (1990)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(L\)-function; Shimura variety; Hilbert-Blumenthal surface; Tate's conjectures for abelian fields; group of algebraic cycles; intersection cohomology; canonical intermediate-perversity extension; Hirzebruch- Zagier cycles; Tate class Gordon, B. B.: Algebraic cycles in families of abelian varieties over Hilbert -- blumenthal surfaces. J. reine angew. Math. 449, 149-171 (1994)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic groups; Lie groups; arithmetic groups; symmetric space; complex surface; local field; Bruhat-Tits theory; arithmetic function; covolume; superrigidity Rémy, Bertrand, Covolume des groupes \(S\)-arithmétiques et faux plans projectifs [d'après Mumford, Prasad, Klingler, Yeung, Prasad-Yeung], Séminaire Bourbaki. Vol. 2007/2008, Astérisque, 978-285629-269-3, 0303-1179, 326, Exp. No. 984, vii, 83-129 (2010), (2009)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) intersection theory; enumerative geometry; tropical geometry; Newton polytope; discriminant; Thom polynomial; toric variety; spherical variety
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) trivial point; tower; curve; number field; rational point; gonality Xavier Xarles, Trivial points on towers of curves, J. Théor. Nombres Bordeaux 25 (2013), no. 2, 477 -- 498 (English, with English and French summaries).
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) group of automorphisms of smooth curve; \(L\)-functions; zeta-functions; Galois covering; class numbers; varieties over finite fields; Betti numbers; rank of the Mordell-Weil group; conjectures of Birch-Swinnerton-Dyer; Tate conjectures on algebraic cycles Kani, No article title, J. Number Theory, 46, 230, (1994)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Giulietti-Korchmáros function field; Hasse-Weil bound; maximal function fields; quotient curves; Galois subfields; genus spectrum Anbar, N.; Bassa, A.; Beelen, P., A complete characterization of Galois subfields of the generalized Giulietti-Korchmáros function field \textit{Finite Fields Appl.}, 48, 318-330, (2017)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Noether's problem; purely transcendental extension; rational extension; fixed field; inverse Galois problem; unramified Brauer group Chu, H.; Hu, S.; Kang, M.; Kunyavskiĭ, B. E., Noether's problem and the unramified Brauer group for groups of order 64, Int. Math. Res. Not., 12, 2329-2366, (2010)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) second fundamental form; complete intersection; field of rational functions
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) noncommutative regular projective curve; noncommutative function field; Auslander-Reiten translation; Picard-shift; ghost group; maximal order over a scheme; ramification; Witt curve; noncommutative elliptic curve; Klein bottle; Fourier-Mukai partner; weighted curve; orbifold Euler characteristic; noncommutative orbifold; tubular curve; finite dimensional algebra; Beilinson theorem Kussin, Dirk, Weighted noncommutative regular projective curves, J. Noncommut. Geom., 10, 4, 1465-1540, (2016)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Noether's problem; meta-abelian group; rational extension of fields; regular action; invariant field; Galois embedding problem I. Michailov, Noether's problem for some groups of order 16n, Acta Arith. 143 (2010), 277\ 290.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) curve; finite field; Jacobian; rational points José Felipe Voloch, Jacobians of curves over finite fields, Rocky Mountain J. Math. 30 (2000), no. 2, 755 -- 759.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Selmer group; isogeny; Abelian variety; Jacobian variety; Galois cohomology Schaefer, E. F.; Wetherell, J. L.: Computing the Selmer group of an isogeny between abelian varieties using a further isogeny to a Jacobian. J. number theory 115, No. 1, 158-175 (2005)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Gelfand-Cetlin system; toric degeneration; Lagrangian intersection Floer theory; potential function Nishinou, T.; Nohara, Y.; Ueda, K., \textit{toric degenerations of Gelfand-cetlin systems and potential functions}, Adv. Math., 224, 648-706, (2010)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) zeta function of Gorenstein ring; singular curve; Gorenstein curve; functional equation; number of rational points on the compactified Jacobian; Riemann hypotheses Karl-Otto Stöhr, Local and global zeta-functions of singular algebraic curves, J. Number Theory 71 (1998), no. 2, 172 -- 202.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) non-commutative surface; noncommutative bundle; intersection theory; Grothendieck group; noncommutative algebraic geometry I. Mori, and, S. P. Smith, The Grothendieck group of a quantum projective space bundle, submitted.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) automorphic form; Picard variety; unitary group; Dolbeault cohomology; theta function Carayol, H., Cohomologie automorphe et compactifications partielles de certaines variétés de Griffiths-schmid, Compos. Math., 141, 1081-1102, (2005)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Abelian varieties; Hodge theory; motives; Diophantine geometry; Gross- Zagier formula; Mordell, Shavarevich and Tate conjectures; height; cristalline cohomology; Arakelov intersection theory
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) linear algebraic group; local field; Bruhat-Tits fixed point theorem
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic group; pseudo-reductive group; pseudo-abelian variety; unipotent group; Weil restriction Totaro, B.\!, Pseudo-abelian varieties, Ann. Sci. École Norm. Sup., 46, 5, 693-721, (2013)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; ranks of the Mordell-Weil groups; ranks of the groups of rational points; Shimura-Taniyama-Weil conjecture; Birch-Swinnerton-Dyer conjecture S. Fermigier, Étude expérimentale du rang de familles de courbes elliptiques sur \(\mathbb{Q}\)
\[
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Chabauty method; Chabauty-Coleman method; Chabauty-Kim method; Mordell's conjecture; Faltings's theorem; rational points; \(p\)-adic height; Selmer varieties; hyperelliptic curves; bielliptic curves; conjectures of Bloch and Kato; Nekovář's \(p\)-adic height pairing; mixed extensions; Mordell-Weil sieve J. S. Balakrishnan and N. Dogra, Quadratic Chabauty and rational points, I: \(p\)-adic heights, preprint, arXiv:1601.00388v2 [math.NT].
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; finite fields; group of rational points
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fibration method; elliptic curves; computation of \(L\)-functions of hyperelliptic curves over the rational function field
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) higher class field theory; local class field theory; Milnor K-group; Galois cohomology; higher global class field theory; Zariski cohomology; p-adic Hodge-Tate theory; Fontaine-Messing theory; Higher ramification theory
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) modular curves; quadratic points; Mordell-Weil; Jacobian; Chabauty
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) BKP flow; Jacobian varieties; conformal field theory; Prym varieties; infinite Grassmannian; BKP hierarchy; dynamical systems Martín, F. J. Plaza: Prym varieties and infinite grassmannians. Int. J. Math. 9, No. 1, 75-93 (1998)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) collected papers; Shafarevich conjecture; normal extensions of a number field; non abelian Galois groups; Galois group is a pro-\(\ell \)-group; class field tower; Mordell conjecture; infinite Lie pseudo-groups; derivations I.M. Gel'fand, in: S.G. Gindikin, V.W. Guillemin, A.A. Kirillov, B. Kostant, S. Sternberg (Eds.), Collected Papers, Vol. III, Springer, Berlin, 1989.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) mirror symmetry conjecture; Schoen's Calabi-Yau 3-fold; complete intersection; toric variety; Yukawa couplings; theta function; eta function; Gromov-Witten invariants Hosono, S., Saito, M-H., Stienstra, J.: On the mirror symmetry conjecture for Schoen's Calabi-Yau 3-folds. In: Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publishing, River Edge, NJ, 1998, pp. 194--235
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) theta functions; topological quantum field theory; Murakami-Ohtsuki-Okada invariant; Chern-Simons theory; Heisenberg group; Schroedinger representation; Segal-Bargmann quantization; Weyl quantization; geometric quantization; exact Egorov identity; skein module 6. R. Gelca, Theta Functions and Knots (World Scientific, Singapore, 2014). [Abstract]
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(K3\) surface; Jacobian fibration; Mordell-Weil lattice K. Nishiyama, Examples of Jacobian fibrations on some K3 surfaces whose Mordell-Weil lattices have the maximal rank 18, Comment. Math. Univ. St. Paul. 44 (1995) 219-223.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) periodic Toda lattice; Jacobian variety; theta divisor; Riemann theta function Kodama, Y.: Topology of the real part of hyperelliptic Jacobian associated with the periodic Toda lattice. Theoret. math. Phys. 133, 1692-1711 (2002)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(G\)-functions; formal power series; linear differential equation; \(p\)- adic differential equations; Padé approximants; general introduction to \(p\)-adic analysis; Dwork's theorem; rationality of the zeta function of a hypersurface over a finite field; \(D\)-modules; Honda's theory of differential equations in finite characteristics; applications to Katz' theorem; Dwork-Robba theorem; Dwork's transfer principles; Chudnovsky's theorem; Dwork-Robba type estimates; growth of solutions at the boundary of a singular disk; nilpotent monodromy; diophantine nature of the exponents; equivalence of Bombieri's and Galochkin's conditions B. \textsc{Dwork}, G. \textsc{Gerotto} and F. \textsc{Sullivan}, \textit{An Introduction to G-Functions}, Annals of Mathematical Studies, vol.~133, Princeton University Press, Princeton, 1994.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) principally polarised abelian variety; moduli space; cohomology of moduli spaces; mapping class group; Torelli group; Morse theory R. Hain, The rational cohomology ring of the moduli space of abelian 3-folds, Math. Res. Lett. 9 (2002), no. 4, 473-491.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational curves; quantum cohomology ring; operads; stable trees; Gromov-Witten invariants; Frobenius manifold; WDVV equation; Künneth formula; intersection theory of the moduli space; stable genus-0 curves with \(n\) marked points Kaufmann, R, The intersection form in \(H^### ({\overline{M}}_{0, n})\) and the explicit Künneth formula in quantum cohomology, Int. Math. Res. Not., 19, 929-952, (1996)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) function field of one variable over a finite field; group of divisor classes; upper bound; zeta-function
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) diophantine geometry; height functions; rational points; abelian varieties; Mordell-Weil theorem; diophantine approximation; Roth's theorem; Siegel theorem; Bombieri's proof of Mordell's conjecture Hindry, Marc; Silverman, Joseph H., Diophantine geometry\upshape, An introduction, Graduate Texts in Mathematics 201, xiv+558 pp., (2000), Springer-Verlag, New York
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic variety; rational points; bounded height; counting function; Manin's conjecture; determinant method; circle method; del Pezzo surfaces Browning, T. D., Quantitative Arithmetic of Projective Varieties, (2009), Birkhäuser, Basel
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) quadratic form; function field of a quadric; stably birational equivalence; motivic equivalence; similarity; half-neighbor; Chow group; correspondence N. Karpenko, Izhboldin's results on stably birational equivalence of quadrics, Lecture Notes in Mathematics 1835 (2004), 151--183.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic number theory; algebraic function fields; local class field theory; ramification theory; differentials; arithmetic curves Artin, E.: Algebraic Numbers and Algebraic Functions. AMS Chelsea Publishing, Providence, RI (2006)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational curves; stable algebraic curves; quantum cohomology of a complex projective algebraic manifold; cohomological field theory; variation of Hodge structures; mirror dual manifold; Gromov-Witten classes; operads for moduli spaces of stable curves M. Kontsevich and Y. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), no. 3, 525-562.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational points; Brauer-Manin obstruction; global function field; strong approximation; torus Liu, Qing and Xu, Fei Very strong approximation for certain algebraic varieties \textit{Math. Ann.}363 (2015) 701--731 Math Reviews MR3412340
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) group of rational points; elliptic curve; complex multiplication; p-adic L-function Tilouine, J. : Fonctions L p-adiques à deux variables et Z2p-extensions . Bull. Soc. Math. France 114 (1986), 3-66.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite field; Hasse-Weil bound; Stöhr-Voloch theory; maximal curve
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Witt group; function field; residue homomorphism; kernel; cokernel; hyperelliptic curves Parimala, R., Sujatha, R.: Witt groups of hyperelliptic curves. Comment. Math. Helvetici65, 559--580 (1990)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) hyperelliptic function; elliptic function; sigma function; reduction of hyperelliptic functions; Jacobian variety of an algebraic curve
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil base; elliptic curve; Frobenius; Selmer group
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Brauer group of a variety; unramified Brauer group; local field; hyperelliptic curve; quaternion algebras Margolin G. L., Quaternion Generation of the 2-torsion Part of the Brauer Group of a Local Quintic
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) spinor group; prehomogeneous vector space; half-spin representation; irreducible relative invariant; Haar measure; representation space; meromorphic function; \(p\)-adic local field; real poles; \(b\)-function Zhu, X. -W.: The classification of spinors under gspin14 over finite fields. Trans. amer. Math. soc. 333, 95-114 (1992)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) infinitely near points; algebraic group actions; field of invariant rational functions; rationality of moduli spaces of pointed plane curves Mazouni, A, Quotient de la variété des points infiniment voisins d'ordre 9 sous l'action de \(PGL_{3}\), Bull. SMF, 124, 425-455, (1996)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) quadratic forms; function field of a quadric; spinor norm; Galois cohomology; unramified cohomology; étale cohomology; Chow group; spectral sequence B. Kahn and R. Sujatha, Unramified cohomology of quadrics II, Duke Mathematical Journal 106 (2001), 449--484.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) effective divisor; fundamental group; Arakelov divisor; Arakelov geometry; Arakelov intersection theory; arithmetic surfaces; Green functions Bost, J. B., Potential theory and Lefschetz theorems for arithmetic surfaces, Ann. Sci. Éc. Norm. Supér. (4), 32, 241-312, (1999)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) complex curve; Riemann surface; theta function; Schottky problem; Jacobian variety; quartics; quintics
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) weighted cohomology groups; weight profile; reductive Borel-Serre compactification; arithmetic group; intersection cohomology groups; topological trace formula; fixed point formula; Lefschetz number; Hecke correspondence Goresky, M.; Harder, G.; Macpherson, R., \textit{weighted cohomology}, Invent. Math., 116, 139-213, (1994)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hodge theory; log geometry; intermediate Jacobian; Néron model; admissible normal function; zero locus Kato, K., Nakayama, C., Usui, S.: Analyticity of the closures of some Hodge theoretic subspaces (2011). arXiv:1102.3528
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) existence of rational point; projective plane with four points in general position blown-up; Grassmannian variety A.N. Skorobogatov , On a theorem of Enriques-Swinnerton-Dyer . Ann. Fac. Sci. Toulouse Math. ( 6 ) 2 ( 1993 ), n^\circ 3 , 429 - 440 . Numdam | MR 1260765 | Zbl 0811.14020
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Jacobian variety; rational torsion; torsion divisor; continued fraction expansion; hyperelliptic curves
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) group schemes; arithmetic groundfields; degenerations of abelian varieties; arithmetic compactifications for the moduli spaces; principally polarized abelian varieties; geometric invariant theory; deformation theory; algebraization of formal moduli; Satake-Baily-Borel compactification; toroidal compactification; degenerations of polarized abelian varieties; polarizations; algebraic stack; Shimura varieties; equivariant sheaves; Hodge theory; De Rham cohomology; crystalline cohomology; action of Hecke operators; conformal quantum field theory G. \textsc{Faltings} and C.-L. \textsc{Chai}, \textit{Degeneration of Abelian Varieties}, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol.~22, Springer, Berlin, 1990, with an Appendix by David Mumford.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) intersection of two quadrics; Tate-Shafarevich group; descent theory Sir, P. Swinnerton-Dyer: Rational points on certain intersections of two quadrics. Abelian varieties, 273-292 (1995)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Drinfeld modules; elliptic modules; cyclotomic function fields; congruence function fields; Carlitz modules; nonarchimedean analysis; explicit class field theory; Gauss sums; Gamma and Zeta functions and values; Jacobi sums; diophantine approximation; \(t\)-modules; \(t\)-motives; transcendence and irrationality; automata and algebraicity D.S. Thakur, \(Function Field Arithmetic\), World Scientfic, Singapore, 2004.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) p-adic height; rational point on elliptic curve over number field; good reduction B. Perrin-Riou, Sur les hauteurs \(p\)-adiques , C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 6, 291-294.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) maximal function field; Hermitian function field; automorphism group Garcia, A.; Stichtenoth, H.; Xing, C. P., On subfields of the Hermitian function field, \textit{Comp. Math.}, 120, 137-170, (2000)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) finite field; hyperelliptic curve; genus; rational point Kurlberg, Pär; Rudnick, Zeév, The fluctuations in the number of points on a hyperelliptic curve over a finite field, J. number theory, 129, 3, 580-587, (2009)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912).
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) higher \(K\)-theory; hyperelliptic Jacobian; Jacobian variety; Quillen group; Griffiths' infinitesimal invariant Collino, A., Griffiths' infinitesimal invariant and higher \(K\)-theory on hyperelliptic Jacobians, J. Alg. Geom. 6 (1997), 393-415.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic function field; group of automorphisms; finiteness; Weierstrass points Schmid, Über die Automorphismen eines algebraischen Funktionenkörpers von Primzahlcharakteriatik., J. reine angew. Math. 179 pp 5-- (1938)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) sections of fibrations; Mordell-Weil groups; rational surfaces
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Arakelov divisor; pure cubic field; size function; Hermitian line bundle; Picard group Francini, P., The size function \(h^\circ\) for a pure cubic field, Acta Arith., 111, 3, 225-237, (2004)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) connected semi-simple complex algebraic group; maximal unipotent subgroup; finite-dimensional representation; G-orbit; normal variety with rational singularities M. BRION , Sur certaines représentations des groupes semi-simples (C.R. Acad. Sc., t. 296, série I, 1983 , p. 5-6). MR 84b:14027 | Zbl 0538.14007
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) conformal field theories of free fermions; bosonization; Jacobian of a compact Riemann surface; formal groups; Hirota tau function; fermion Fock space
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fundamental group of a curve; \(\ell\)-adic representations; Langlands conjectures; field of rational functions on a curve; Dirichlet series Drinfed, V. G., \textit{two-dimensional \textit{\(\mathcal{l}\)}-adic representations of the fundamental group of a curve over a finite field and automorphic forms on \textbf{GL}(2)}, Amer. J. Math., 105, 85-114, (1983)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) moduli space of curves; Cohomological Field Theory; Topological Field Theory; Batalin-Vilkovisky algebra; operads; Givental group action [DSV13] V. Dotsenko, S. Shadrin &aB. Vallette, &Givental group action on topological field theories and homotopy Batalin-Vilkovisky algebras­vances in Math.236 (2013), p. 224-MR 30 | &Zbl 1294.
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) intersection theory; geometric invariant theory; K-moduli spaces; Weil-Petersson geometry
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational point; jacobian Leprévost, Famille de courbes de genre 2 munies d'une classe de diviseurs rationnels d'ordre 13, C. R. Acad. Sci. Paris Sér. I Math. 313 pp 451-- (1991)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic surfaces; intersection theory; singularities; ruled surfaces; quasielliptic fibrations; minimal model theory; canonical dimension; Enriques-Kodaira classification of algebraic surfaces; characteristic \(p\); elliptic fibrations; rational surfaces Bădescu, L., Algebraic surfaces, Universitext, (2001), Springer-Verlag New York, Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author. MR 1805816
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) optimal curve; algebraic-geometric code; function field; automorphism group of AG-code
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) compactifications; \(({\mathbb P}^ 1)^ r\); quotient of the complex r-ball by discrete subgroups of PU(r,1); desingularizations; Betti numbers; Hodge numbers; \(L^ 2\)-cohomology; rational cohomology; Poincaré polynomial; intersection homology; group cohomology Kirwan F.C., Lee R., Weintraub S.H.: Quotients of the complex ball by discrete groups. Pac. J. Math. 130, 115--141 (1987)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Heights, Weil height machine; ample divisors; effective divisors; intersection theory Dinh, T.-C., Sibony, N.: Density of positive currents and dynamica of Hénon type automorphism of \(\mathbb{C}^k\). Preprint arXiv:1203.5810 (2012)
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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) L-functions; Beilinson conjecture; Bloch conjecture; Shimura variety; quaternionic algebra; Jacquet-Langlands theory; isogeny between the corresponding parts of the Jacobian varieties; K-cohomology groups; regulator maps D. Ramakrishnan, Higher regulators on quaternionic Shimura curves and values of \(L\)-functions , Applications of algebraic \(K\)-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 377-387.
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