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

This entry is about a section of the text

• Michel Demazure, lectures on p-divisible groups, web

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

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