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

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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.


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)

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