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Mathematics > Representation Theory
Title: The integral motivic Satake equivalence for ramified groups
(Submitted on 24 Apr 2024)
Abstract: We construct the geometric Satake equivalence for quasi-split reductive groups over nonarchimedean local fields, using \'etale Artin-Tate motives with $\mathbb{Z}[\frac{1}{p}]$-coefficients. We consider local fields of both equal and mixed characteristic. Along the way, we extend the work of Gaussent--Littelmann on the connection between LS galleries and MV cycles to the case of residually split reductive groups. As an application, we generalize Zhu's integral Satake isomorphism for spherical Hecke algebras to ramified groups. Moreover, for residually split groups, we define generic spherical Hecke algebras, and construct generic Satake and Bernstein isomorphisms.
Submission history
From: Thibaud Van Den Hove [view email][v1] Wed, 24 Apr 2024 07:03:46 GMT (84kb)
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