A Deligne-Lusztig type correspondence for tame p-adic groups

2023/06/03 by Zhongyipan Lin, Lin, Zhongyipan · 1 citation
Mathematics · #11S20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.02093

openalex publication_date 2023/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results concerning mod p Langlands parameters for quasi-split tame groups G over a p-adic field F: (1) semisimple L-parameters Gal_F→ ^ L G(\mathbbF_p) factor through the L-group of a maximal F-torus of G; (2) All semisimple mod p L-parameters admit a de Rham lift of regular p-adic Hodge type; (3) A version of tame inertial local Langlands correspondnece; and (4) A group-theoretic description of irreducible components of the reduced Emerton-Gee stacks away from Steinberg parts. We also propose generalizations of the explicit recipe for Serre weights (after Herzig) and the geometric Breuil-Mézard for tame groups.

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• The topological Breuil-Mézard conjecture for classical groups

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