Chtoucas restreints pour les groupes réductifs et paramétrisation de Langlands locale

2017/09/04 by Alain Genestier, Genestier, Alain, Vincent Lafforgue +1 · 1 citation
Mathematics · #11F70 #11S37 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:11F70 #msc:11S37 #msc:14G35

paper · pdf · doi:10.48550/arxiv.1709.00978

in French

openalex publication_date 2017/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We associate to every irreducible representation of a reductive group over a local field of equal characteristics a local Langlands parameter up to semisimplification and prove the compatibility with the global parameterization constructed by the second author. Our method involves stacks of restricted shtukas (which are analogues of truncated Barsotti-Tate groups) and nearby cycles over arbitrary bases.

Cited by

• Geometric Satake, categorical traces, and arithmetic of Shimura varieties

Related

• Introduction to chtoucas for reductive groups and to the global Langlands parameterization
• Representations of reductive groups over local fields
• Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale
• A `relative' local Langlands correspondence
• Langlands parameters for reductive groups over finite fields