Introduction to chtoucas for reductive groups and to the global Langlands parameterization

Abstract

This is a translation in English of version 5 of the article arXiv:1404.3998, which is itself an introduction to arXiv:1209.5352. We explain all the ideas of the proof of the following theorem. 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.

References in corpus (2)

• Twisted geometric Satake equivalence: reductive case
• Introduction aux chtoucas pour les groupes réductifs et à la paramétrisation de Langlands globale

Cited by in corpus (2)

• Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate $(\phi ,\Gamma )$-modules
• Acceptable compact Lie groups