Chtoucas restreints pour les groupes r\'eductifs et param\'etrisation de Langlands locale

TL;DR

This paper develops a new local Langlands correspondence for reductive groups over local fields of equal characteristic, using stacks of restricted shtukas and nearby cycles, and proves compatibility with global parameters.

Contribution

It introduces a novel approach to associate local Langlands parameters to irreducible representations using stacks of restricted shtukas, extending existing theories.

Findings

Constructs local Langlands parameters for all irreducible representations.

Establishes compatibility with global Langlands parameterization.

Utilizes stacks of restricted shtukas and nearby cycles in the proof.

Abstract

We associate to every irreducible representation of a reductive group over a local field of equal characteristics a local Langlands parameter up to semisimplification and prove the compatibility with the global parameterization constructed by the second author. Our method involves stacks of restricted shtukas (which are analogues of truncated Barsotti-Tate groups) and nearby cycles over arbitrary bases.