over $R$ [\[EGA $\textsc{III}_{2}$, 7.8.6, p.206\]]{}.

(3) If $R$, respectively $T$, is an ${\mathds{F}}_p$-algebra, respectively ${\mathds{F}}_p$-scheme, we write $F_R:R\to R$, respectively $F_T:T\to T$, to denote the [*Frobenius morphism*]{}. If $T$ is in addition a scheme over a perfect field, we adopt the notations of [@jantzen87 Part I, 9.1] with the exception that we write ${\rm Fr}^s:M^{(t)}\to M^{(s+t)}$ while Jantzen uses $F_{M^{(t)}}^s:M^{(t)}\to M^{(t+s)}$.

(4) If $R$ is a discrete valuation ring and $y:{\mathrm{Spec}\,}R\to Y$ is an $R$-point of a scheme $Y$, we shall write $y_{\rm gen}$ for the image of the generic point of ${\mathrm{Spec}\,}R$ in $Y$.

(5) Let $X\to S$ be a morphisms of schemes possessing in addition a section $x:S\to X$. Given morphisms ${\varphi}:X'\to X$ and $f:S'\to S$, any morphism of $S$-schemes $x':S'\to X'$ such that ${\varphi}x'=x  f$ shall be called an $S'$-point of $X'$ above $x$. (That is, for the sake of economy we choose not to make base-changes to $S'$.)

 On group schemes {#on-group-schemes .unnumbered}
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(1) To avoid repetitions, “*group scheme*” is a synonym for “*affine group scheme*.” If $G$ is a group scheme over a ring $R$, and $R'$ is an $R$-algebra, we write $R'[G]$ instead of ${{\mathscr{O}}}(R'{\otimes}_RG)$.

(2) The category of flat group schemes 