English

Shtukas for reductive groups and Langlands correspondence for function fields

Algebraic Geometry 2018-03-13 v1 Representation Theory

Abstract

We discuss recent developments in the Langlands program for function fields, and in the geometric Langlands program. In particular we explain a canonical decomposition of the space of cuspidal automorphic forms for any reductive group G over a function field, indexed by global Langlands parameters. The proof uses the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence.

Keywords

Cite

@article{arxiv.1803.03791,
  title  = {Shtukas for reductive groups and Langlands correspondence for function fields},
  author = {Vincent Lafforgue},
  journal= {arXiv preprint arXiv:1803.03791},
  year   = {2018}
}

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ICM report

R2 v1 2026-06-23T00:48:26.130Z