On the other hand, the right hand cohomology group is isomorphic to de Rham cohomology of the complex manifold formula_78 associated to , denoted here formula_103 Yet another classical result, de Rham's theorem, asserts an isomorphism of the latter cohomology group with singular cohomology (or sheaf cohomology) with complex coefficients, formula_104, which by the universal coefficient theorem is in its turn isomorphic to formula_105 Composing these isomorphisms yields two "rational" vector spaces which, after tensoring with formula_106 become isomorphic. Choosing bases of these rational subspaces (also called lattices), the determinant of the base-change matrix is a complex number, well defined up to multiplication by a rational number. Such numbers are "periods".