Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale

Source abstract

For any reductive group G G over a global function field, we use the cohomology of G G -shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G 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.