Endoscopy for Modular Hecke Categories
Representation Theory
2026-04-20 v2
Abstract
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.
Cite
@article{arxiv.2508.10214,
title = {Endoscopy for Modular Hecke Categories},
author = {Colton Sandvik},
journal= {arXiv preprint arXiv:2508.10214},
year = {2026}
}
Comments
101 pages. Many small errors and typos corrected. Exposition improved in many places. Flaw in Whittaker category section corrected with new arguments