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arXiv · 2411.12129

Lagrange's theorem for a family of finite flat group schemes over local Artin rings

Emiliano Torti
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Abstract

Let R be a local Artin ring with residue field k of positive characteristic. We prove that every finite flat group scheme over R whose special fiber belongs to a certain explicit family of non-commutative k-group schemes is killed by its order. This is achieved via a classification result which rely on the explicit study of the infinitesimal deformation theory for such non-commutative k-group schemes. The main result answers positively in a new case a question of Grothendieck in SGA 3 on whether all finite flat group schemes are killed by their order.

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Emiliano Torti. 2024-11-18. Lagrange's theorem for a family of finite flat group schemes over local Artin rings. https://arxiv.org/abs/2411.12129

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