Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale

Vincent Lafforgue

Published 2012-09-24, updated 2015-09-17Version 5

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 direction "from automorphic to Galois". 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.