Endoscopy for Modular Hecke Categories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915941134106624 |
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| author | Sandvik, Colton |
| author_facet | Sandvik, Colton |
| contents | Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's monodromic Hecke category. We then give two applications: (1) a modular categorification of the monodromic Hecke algebra, and (2) a monoidal equivalence between the monodromic Hecke category of parity sheaves and the ordinary Hecke category of parity sheaves on the endoscopic group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_10214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Endoscopy for Modular Hecke Categories Sandvik, Colton Representation Theory 20G20, 14F08, 14F43, 20C08 Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's monodromic Hecke category. We then give two applications: (1) a modular categorification of the monodromic Hecke algebra, and (2) a monoidal equivalence between the monodromic Hecke category of parity sheaves and the ordinary Hecke category of parity sheaves on the endoscopic group. |
| title | Endoscopy for Modular Hecke Categories |
| topic | Representation Theory 20G20, 14F08, 14F43, 20C08 |
| url | https://arxiv.org/abs/2508.10214 |