Minimal truncations of supersingular p-divisible groups

Details Minimal truncations of supersingular p-divisible groups Minimal truncations of supersingular p-divisible groups

2006-06-30

arxiv.org/abs/math/0606777v2

Indiana Univ. Math. J. {\bf 56} (2007), no. 6, pp. 2887-2897

Mathematics

Number Theory

9 pages, LaTex; to appear in Indiana Univ. Math. J

Scientific paper

10.1512/iumj.2007.56.3110

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])).

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