2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167747Let $k$ 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 $k$.8 pages, laTex; to appear in Rend. Sem. Mat. Univ. PadovaNumber TheoryAlgebraic Geometry11G10, 11G18, 14F30, 14G35, 14L05text