Pseudo-rigid p-torsion finite flat commutative group schemes

Let p be a prime number and k a perfect field of characteristic p. In the present paper, we study deformations of finite flat commutative group schemes over k to the ring W of Witt vectors with coefficients in k. We prove that, for a given principally quasi-polarizable p-torsion finite flat commutative group scheme over k, it holds that the group scheme is pseudo-rigid - i.e., roughly speaking, has a unique, up to isomorphism over W, deformation to W - if and only if the group scheme is superspecial. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study demonstrates that for a given principally quasi-polarizable p-torsion finite flat commutative group scheme over a perfect field of characteristic p, the deformation to the ring of Witt vectors is unique to W if and only if the group scheme is superspecial.