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arXiv · 2311.04043

Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic

Johannes Anschütz·João Lourenço·Zhiyou Wu·Jize Yu
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Abstract

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 $E_7$.

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Johannes Anschütz, João Lourenço, Zhiyou Wu, Jize Yu. 2023-11-07. Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic. https://arxiv.org/abs/2311.04043

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