Demazure, lectures on p-divisible groups, II.4, k-formal groups, Cartier duality

This entry is about a section of the text

A *$k$-formal group* is a $k$-group whose underlying $k$-functor is a $k$-formal functor.

The previous constructions in chapter II carry over to $k$-formal groups.

Let $G$ be a commutative $k$-group functor. Then the *Cartier dual* $D(G)$ of $G$ is defined by

$D(G)(R)=Gr_R(G\otimes_k R,\mu_R)$

Moreover we have

$hom(G,D(H))=hom(H,D(G))=hom(G\times H,\mu_k)$

Revised on May 27, 2012 13:30:40
by Stephan Alexander Spahn
(79.227.168.80)