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the Barsotti-Tate group of an abelian variety

Recall that a p-divisible group GG has the defining properties that pid G:GGp \,id_G:G\to G is an epimorphism with finite kernel satisfying G= jkerp jid GG=\cup_j ker\, p^j \, id_G.

Now let AA be any commutative algebraic kk-group such that pid A:AAp\, id_A:A\to A is an epimorphism. Then

A(p):= jkerp jid AA(p):=\cup_j ker \,p^j \,id_A

is a pp-divisible group.

Revised on June 9, 2012 14:29:18 by Stephan Alexander Spahn (79.227.138.186)