Geometric structure and the local Langlands conjecture

2012/11/01 by Anne‐Marie Aubert, Aubert, Anne-Marie, Paul Baum +5
Mathematics · #20G05 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1211.0180

openalex publication_date 2012/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive p-adic group. The method of proof is to establish the presence of a very simple geometric structure, in both the smooth dual and the Langlands parameters. We prove that this geometric structure is present, in the same way, for the general linear group, including all of its inner forms. With these results as evidence, we give a detailed formulation of a general geometric structure conjecture.

Citations

• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

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