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Minimal truncations of supersingular p-divisible groups

Marc-Hubert Nicole·Adrian Vasiu
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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 λ, we show that (H,λ) 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],λ[p^d])).

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Marc-Hubert Nicole, Adrian Vasiu. 2007-07-06. Minimal truncations of supersingular p-divisible groups. https://doi.org/10.1512/iumj.2007.56.3110

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