Traverso's isogeny conjecture for p-divisible groups

Details Traverso's isogeny conjecture for p-divisible groups Traverso's isogeny conjecture for p-divisible groups

2006-06-30

arxiv.org/abs/math/0606780v3

Rend. Semin. Mat. Univ. Padova 118 (2007), 73--83

Mathematics

Number Theory

8 pages, laTex; to appear in Rend. Sem. Mat. Univ. Padova

Scientific paper

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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