Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale

2012/09/24 by Lafforgue, Vincent · 3 citations
#11F70 #14G35 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1209.5352

Abstract

For any reductive group G over a global function field, we use the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the "automorphic to Galois" direction. Moreover we obtain a canonical decomposition of the spaces of cuspidal automorphic forms indexed by global Langlands parameters. The proof does not rely at all on the Arthur-Selberg trace formula.

Cited by

• Local and global Langlands conjecture(s) over function fields
• Deformations of pseudocharacters and Mazur's finiteness condition
• Modular intersection cohomology of Drinfeld's compactifications

Related

• Introduction aux chtoucas pour les groupes r 'eductifs et `a la\n param 'etrisation de Langlands globale
• Introduction to chtoucas for reductive groups and to the global Langlands parameterization
• Shtukas for reductive groups and Langlands correspondence for function\n fields
• Chtoucas restreints pour les groupes réductifs et paramétrisation de Langlands locale
• Potential automorphy of \widehatG-local systems