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

Vincent Lafforgue (1)

1 IF - Institut Fourier

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.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Vincent Lafforgue. Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale. Journal of the American Mathematical Society, 2018, 31 (3), pp.719-891. ⟨10.1090/jams/897⟩. ⟨hal-01144808⟩