article

Title: Minimal truncations of supersingular $p$-divisible groups

Authors: Marc-Hubert Nicole and Adrian Vasiu

Issue: Volume 56 (2007), Issue 6, 2887-2898

Abstract:

$Let $k$ be an algebraically closed field of characteristic $p > 0$. Let $H$ be a supersingular $p$-divisible group over $k$ of height $2d$. We show that $H$ is uniquely determined up to isomorphism by its truncation of level $d$ (i.e., by $H[p^d]$). This proves Traverso's truncation conjecture for supersingular $p$-divisible groups. If $H$ has a principal quasi-polarization $\lambda$, we show that $(H, \lambda)$ is also uniquely determined up to isomorphism by its principally quasi-polarized truncated Barsotti-Tate group of level $d$ (i.e., by $(H[p^d], \lambda[p^d])$).$