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

@article{Lafforgue2012ChtoucasPL,
  title={Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale},
  author={V. Lafforgue},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
  • V. Lafforgue
  • Published 2012
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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. 
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