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Hi,

Let $k$ be a perfect field of characteristic $p > 0$. Let $A/k$ be an abelian variety. Then the first crystalline cohomology group of $A$ with respect to $W(k)$ (= Witt vectors) is canonically isomorphic to the (contravariant) Dieudonne functor of the $p$-divisible group of $A$.

This is well-known result and I am wondering if there is a simple proof of it. Specifically, I am wondering if there is a proof that doesn't require defining the Dieudonne crystal for a $p$-divisible group as an intermediary.

Thanks!

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  • $\begingroup$ I am also interested in this question. I know the reference Mazur-Messing, but this is quite lengthy. $\endgroup$
    – user19475
    Jul 8, 2013 at 16:04
  • $\begingroup$ Can someone push this question up? $\endgroup$
    – user19475
    Jul 8, 2013 at 16:08

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