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Traverso's isogeny conjecture for p-divisible groups

Marc-Hubert Nicole·Adrian Vasiu
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Abstract

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $c,d\in\dbN$. Let $b_{c,d}\ge 1$ be the smallest integer such that for any two $p$-divisible groups $H$ and $H^\prime$ over $k$ of codimension $c$ and dimension $d$ the following assertion holds: If $H[p^{b_{c,d}}]$ and $H^\prime[p^{b_{c,d}}]$ are isomorphic, then $H$ and $H^\prime$ are isogenous. We show that $b_{c,d}=\lceil{cd\over {c+d}}\rceil$. This proves Traverso's isogeny conjecture for $p$-divisible groups over $k$.

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Marc-Hubert Nicole, Adrian Vasiu. 2007-01-18. Traverso's isogeny conjecture for p-divisible groups. https://arxiv.org/abs/math/0606780

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