Hecke operators for curves over non-archimedean local fields and related finite rings
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915417049530368 |
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| author | Braverman, Alexander Kazhdan, David Polishchuk, Alexander Wong, Ka Fai |
| author_facet | Braverman, Alexander Kazhdan, David Polishchuk, Alexander Wong, Ka Fai |
| contents | We study Hecke operators associated with curves over a non-archimedean local field $K$ and over the rings $O/{\mathfrak m}^N$, where $O\subset K$ is the ring of integers. Our main result is commutativity of a certain "small" local Hecke algebra over $O/{\mathfrak m}^N$, associated with a connected split reductive group $G$ such that $[G,G]$ is simple and simpy connected. The proof uses a Hecke algebra associated with $G(K(\!(t)\!))$ and a global argument involving $G$-bundles on curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09595 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hecke operators for curves over non-archimedean local fields and related finite rings Braverman, Alexander Kazhdan, David Polishchuk, Alexander Wong, Ka Fai Number Theory Algebraic Geometry Representation Theory We study Hecke operators associated with curves over a non-archimedean local field $K$ and over the rings $O/{\mathfrak m}^N$, where $O\subset K$ is the ring of integers. Our main result is commutativity of a certain "small" local Hecke algebra over $O/{\mathfrak m}^N$, associated with a connected split reductive group $G$ such that $[G,G]$ is simple and simpy connected. The proof uses a Hecke algebra associated with $G(K(\!(t)\!))$ and a global argument involving $G$-bundles on curves. |
| title | Hecke operators for curves over non-archimedean local fields and related finite rings |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2305.09595 |