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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.16067 |
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| _version_ | 1866913810851299328 |
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| author | Mehidi, Sara |
| author_facet | Mehidi, Sara |
| contents | Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$.
In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the curves in the case when the structural $K$-group scheme of the torsor admits a finite flat model over $R$. In this paper, we first give a simpler description of the problem in the case where the curve is semistable. Secondly, if $R$ is assumed to be Henselian and Japanese, we solve the problem of extending torsors even if the structural group does not admit a finite flat $R$-model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16067 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extending torsors under quasi-finite flat group schemes Mehidi, Sara Algebraic Geometry Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$. In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the curves in the case when the structural $K$-group scheme of the torsor admits a finite flat model over $R$. In this paper, we first give a simpler description of the problem in the case where the curve is semistable. Secondly, if $R$ is assumed to be Henselian and Japanese, we solve the problem of extending torsors even if the structural group does not admit a finite flat $R$-model. |
| title | Extending torsors under quasi-finite flat group schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2211.16067 |