Étale geometry of closures of Jordan classes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913973809446912 |
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| author | Ambrosio, Filippo |
| author_facet | Ambrosio, Filippo |
| contents | Let $G$ be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point $g$ in the closure of a Jordan class of $G$ in terms of Jordan classes of a maximal rank reductive subgroup $M \leq G$ depending on the point $g$, and further to the closures of certain decomposition classes in Lie($M$). We adapt this method to the case of an algebraically closed field of characteristic $p$, and we give sufficient restrictions on $p$ for it to hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Étale geometry of closures of Jordan classes Ambrosio, Filippo Representation Theory Algebraic Geometry Group Theory 20G15 (Primary) 17B45, 14L30 (Secondary) Let $G$ be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point $g$ in the closure of a Jordan class of $G$ in terms of Jordan classes of a maximal rank reductive subgroup $M \leq G$ depending on the point $g$, and further to the closures of certain decomposition classes in Lie($M$). We adapt this method to the case of an algebraically closed field of characteristic $p$, and we give sufficient restrictions on $p$ for it to hold. |
| title | Étale geometry of closures of Jordan classes |
| topic | Representation Theory Algebraic Geometry Group Theory 20G15 (Primary) 17B45, 14L30 (Secondary) |
| url | https://arxiv.org/abs/2411.07748 |