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 commutat...

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Bibliographic Details
Published in:Journal of number theory 2021-12, Vol.229, p.261-276
Main Author: Hoshi, Yuichiro
Format: Article
Language:English
Subjects:
Finite flat commutative group scheme
Pseudo-rigid
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Summary: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.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2021.04.026