Introduction aux chtoucas pour les groupes r\'eductifs et \`a la param\'etrisation de Langlands globale

TL;DR

This paper introduces a geometric approach to the global Langlands correspondence for reductive groups over function fields, using shtukas and the geometric Satake equivalence, avoiding trace formula reliance.

Contribution

It provides a new proof of the global Langlands correspondence for reductive groups over function fields via geometric methods involving shtukas and Satake equivalence.

Findings

Establishes the global Langlands correspondence in the automorphic to Galois direction.

Provides a canonical decomposition of cuspidal automorphic forms by Langlands parameters.

Proves the correspondence without using the Arthur-Selberg trace formula.

Abstract

This is an introduction to the article "Chtoucas pour les groupes r\'eductifs et param\'etrisation 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.