Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale

TL;DR

This paper establishes the global Langlands correspondence for reductive groups over function fields using geometric methods, providing a canonical decomposition of automorphic forms without trace formula reliance.

Contribution

It introduces a new geometric approach to prove the global Langlands correspondence for reductive groups over function fields, avoiding traditional trace formula techniques.

Findings

Proves the global Langlands correspondence for G over function fields.

Provides a canonical decomposition of cuspidal automorphic forms.

Uses cohomology of G-shtukas and geometric Satake equivalence.

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.