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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.


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I am also interested in this question. I know the reference Mazur-Messing, but this is quite lengthy. – Timo Keller Jul 8 '13 at 16:04
Can someone push this question up? – Timo Keller Jul 8 '13 at 16:08

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