On simple groups definable in some valued fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908761518505984 |
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| author | Gismatullin, Jakub Halupczok, Immanuel Macpherson, Dugald |
| author_facet | Gismatullin, Jakub Halupczok, Immanuel Macpherson, Dugald |
| contents | We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to live in the home sort. We have a similar result in pure algebraically closed valued fields of positive characteristic, under the additional assumption that the definable group is a subgroup of a linear algebraic group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08423 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On simple groups definable in some valued fields Gismatullin, Jakub Halupczok, Immanuel Macpherson, Dugald Logic Commutative Algebra Algebraic Geometry Group Theory 03C60 20G07 12J10 20E32 We prove that non-abelian definable, definably simple groups in 1-h-minimal henselian valued fields are essentially already linear algebraic groups. Here, the group is assumed to live in the home sort. We have a similar result in pure algebraically closed valued fields of positive characteristic, under the additional assumption that the definable group is a subgroup of a linear algebraic group. |
| title | On simple groups definable in some valued fields |
| topic | Logic Commutative Algebra Algebraic Geometry Group Theory 03C60 20G07 12J10 20E32 |
| url | https://arxiv.org/abs/2601.08423 |