Introduction to chtoucas for reductive groups and to the global Langlands parameterization
Algebraic Geometry
2017-12-27 v4 Representation Theory
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.
Cite
@article{arxiv.1404.6416,
title = {Introduction to chtoucas for reductive groups and to the global Langlands parameterization},
author = {Vincent Lafforgue},
journal= {arXiv preprint arXiv:1404.6416},
year = {2017}
}