Introduction aux chtoucas pour les groupes réductifs et à la paramétrisation de Langlands globale

Abstract

This is an introduction to the article "Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale", arXiv:1209.5352. We explain all the ideas of the proof. 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.

in French. arXiv admin note: substantial text overlap with arXiv:1209.5352

Cited by in corpus (1)

• Introduction to chtoucas for reductive groups and to the global Langlands parameterization