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

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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.

###### Definition

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

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

Last revised on May 27, 2012 at 13:30:40. See the history of this page for a list of all contributions to it.