Vincent Lafforgue
Published 2018-03-10Version 1
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.
Introduction aux chtoucas pour les groupes réductifs et à la paramétrisation de Langlands globale
Log Fano varieties over function fields of curves
Isotriviality is equivalent to potential good reduction for endomorphisms of ${\mathbb P}^N$ over function fields
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