Shtukas for reductive groups and Langlands correspondence for function\n fields

2018/03/10 by Vincent Lafforgue, Lafforgue, Vincent · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1803.03791

Abstract

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

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