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Mathematics > Number Theory
Title: Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence in mixed characteristic
(Submitted on 7 Nov 2023 (v1), last revised 26 Apr 2024 (this version, v2))
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 type $A$ groups.
Submission history
From: João Lourenço [view email][v1] Tue, 7 Nov 2023 14:54:47 GMT (77kb)
[v2] Fri, 26 Apr 2024 08:50:31 GMT (79kb)
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