Shtukas for reductive groups and Langlands correspondence for function fields

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.

ICM report

Cited by in corpus (2)

• Coherent Springer theory and the categorical Deligne-Langlands correspondence
• The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support