Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914006423306240 |
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| author | Anschütz, Johannes Lourenço, João Wu, Zhiyou Yu, Jize |
| author_facet | Anschütz, Johannes Lourenço, João Wu, Zhiyou Yu, Jize |
| contents | We show that the nearby cycles functor for the $p$-adic Hecke stack at parahoric level is perverse t-exact, by developing a theory of Wakimoto filtrations at Iwahori level, and that it lifts to the $\mathbb{E}_1$-center. We apply these tools to construct the Arkhipov-Bezrukavnikov functor for $p$-adic affine flag varieties at Iwahori level, and prove that it is an equivalence for all classical groups and also exceptional groups of type $E_6$ and $E_7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic Anschütz, Johannes Lourenço, João Wu, Zhiyou Yu, Jize Number Theory Algebraic Geometry Representation Theory 14M15 (primary), 13K05, 14L15, 20C08 (secondary) We show that the nearby cycles functor for the $p$-adic Hecke stack at parahoric level is perverse t-exact, by developing a theory of Wakimoto filtrations at Iwahori level, and that it lifts to the $\mathbb{E}_1$-center. We apply these tools to construct the Arkhipov-Bezrukavnikov functor for $p$-adic affine flag varieties at Iwahori level, and prove that it is an equivalence for all classical groups and also exceptional groups of type $E_6$ and $E_7$. |
| title | Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic |
| topic | Number Theory Algebraic Geometry Representation Theory 14M15 (primary), 13K05, 14L15, 20C08 (secondary) |
| url | https://arxiv.org/abs/2311.04043 |