D\'ecomposition au-dessus des param\`etres de Langlands elliptiques

TL;DR

This paper establishes a formula linking cuspidal cohomology groups of moduli stacks of shtukas to representations of the centralizer of elliptic Langlands parameters, advancing the understanding of Arthur-Kottwitz conjectures.

Contribution

It provides a novel formula connecting cohomology of shtukas to centralizer representations for elliptic Langlands parameters, a step towards Arthur-Kottwitz conjectures.

Findings

Cohomology groups are expressed via finite dimensional representations.

The work applies to elliptic global Langlands parameters.

Progress towards Arthur-Kottwitz conjectures.

Abstract

We prove that, over any elliptic global Langlands parameter $\sigma$, the cuspidal cohomology groups of moduli stacks of shtukas are given by a formula involving a finite dimensional representation of the centralizer of $\sigma$. It is a first step in the direction of Arthur-Kottwitz conjectures.