# nLab the Barsotti-Tate group of an abelian variety

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

Now let $A$ be any commutative algebraic $k$-group such that $p\, id_A:A\to A$ is an epimorphism. Then

$A(p):=\cup_j ker \,p^j \,id_A$

is a $p$-divisible group.

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