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Shtukas for reductive groups and Langlands correspondence for function fields (1803.03791v1)
Published 10 Mar 2018 in math.AG and math.RT
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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