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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.12129 |
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| _version_ | 1866912124240920576 |
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| author | Torti, Emiliano |
| author_facet | Torti, Emiliano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrange's theorem for a family of finite flat group schemes over local Artin rings Torti, Emiliano Number Theory Algebraic Geometry 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. |
| title | Lagrange's theorem for a family of finite flat group schemes over local Artin rings |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2411.12129 |