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

This entry is about a section of the text

A kk-formal group is a kk-group whose underlying kk-functor is a kk-formal functor.

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

Definition

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

D(G)(R)=Gr R(G kR,μ R)D(G)(R)=Gr_R(G\otimes_k R,\mu_R)

Moreover we have

hom(G,D(H))=hom(H,D(G))=hom(G×H,μ k)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)