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arXiv · 1803.03791

Shtukas for reductive groups and Langlands correspondence for function fields

Vincent Lafforgue
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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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Vincent Lafforgue. 2018-03-10. Shtukas for reductive groups and Langlands correspondence for function fields. https://arxiv.org/abs/1803.03791

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