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.

中文翻译：

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伪刚性p-扭转有限平面可交换群方案

设p为素数，k为特征p的完美域。在本论文中，我们研究了有限平坦交换群方案的变形超过ķ到环W¯¯维特矢量与系数ķ。我们证明，对于k 上给定的主要可极化p扭转有限平面交换群方案，它认为该群方案是伪刚性的——即，粗略地说，在W 上具有唯一的、高达同构的变形为W——当且仅当组方案是超特殊的。