Minimal truncations of supersingular $p$-divisible groups Marc-Hubert NicoleAdrian Vasiu 11G1011G1814L05supersingular p-divisible groupstruncated Barsotti-Tate groupspolarizationsDieudonn'e modulesaffine group schemes 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 $(H[p^d], \lambda[p^d])$). Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3110 10.1512/iumj.2007.56.3110 en Indiana Univ. Math. J. 56 (2007) 2887 - 2898 state-of-the-art mathematics http://iumj.org/access/