p-adic Cherednik algebras on rigid analytic spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914315101011968 |
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| author | Vázquez, Fernando Peña |
| author_facet | Vázquez, Fernando Peña |
| contents | Let $X$ be a smooth rigid space with an action of a finite group $G$ satisfying that $X/G$ is represented by a rigid space. We construct sheaves of $p$-adic Cherednik algebras on the small étale site of the quotient $X/G$, and study some of their properties. The sheaves of $p$-adic Cherednik algebras are sheaves of Fréchet-Stein $K$-algebras on $X/G$, which can be regarded as $p$-adic analytic versions of the sheaves of Cherednik algebras associated to the action of a finite group on a smooth algebraic variety defined by P. Etingof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-adic Cherednik algebras on rigid analytic spaces Vázquez, Fernando Peña Number Theory Algebraic Geometry Quantum Algebra Rings and Algebras Representation Theory 14G2 (Primary) 81R60 (Secondary) Let $X$ be a smooth rigid space with an action of a finite group $G$ satisfying that $X/G$ is represented by a rigid space. We construct sheaves of $p$-adic Cherednik algebras on the small étale site of the quotient $X/G$, and study some of their properties. The sheaves of $p$-adic Cherednik algebras are sheaves of Fréchet-Stein $K$-algebras on $X/G$, which can be regarded as $p$-adic analytic versions of the sheaves of Cherednik algebras associated to the action of a finite group on a smooth algebraic variety defined by P. Etingof. |
| title | p-adic Cherednik algebras on rigid analytic spaces |
| topic | Number Theory Algebraic Geometry Quantum Algebra Rings and Algebras Representation Theory 14G2 (Primary) 81R60 (Secondary) |
| url | https://arxiv.org/abs/2504.16689 |