Work

Extremal weights and a tameness criterion for mod $p$ Galois representations

Year: 2024

Type: article

Abstract: We study the weight part of Serre’s conjecture for generic n -dimensional mod p Galois representations. We first generalize Herzig’s conjecture to the case where the field is ramified at p and prove the weight elimination direction of the conjecture. We then introduce a new class of weights associated to n -dimensional local mod p representations which we call extremal weights . Using a “Levi reduction” property of certain potentially crystalline Galois deformation spaces, we prove the modularity of these weights. As a consequence, we deduce the weight part of Serre’s conjecture for unit groups of some division algebras in generic situations.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1513

Authors: Daniel Le, Bao Viet Le Hung, Brandon Levin, Stefano Morra

Institutions: Purdue University West Lafayette, Northwestern University, Rice University, Université Paris 8

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4402273241

FWCI: 1.313

Cites:

Cited by: 2

Related to: 10