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.
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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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