Donn\'ees endoscopiques d'un groupe r\'eductif connexe: applications d'une construction de Langlands

TL;DR

This paper proves the equivalence of endoscopic data for connected reductive groups over global fields and describes elliptic endoscopic data for quasi-simple simply connected groups, contributing to the Langlands program.

Contribution

It establishes the equivalence of endoscopic data almost everywhere and provides a detailed description of elliptic endoscopic data for specific groups.

Findings

Equivalence of endoscopic data almost everywhere

Extension of results to endoscopy with character

Description of elliptic endoscopic data for quasi-simple simply connected groups

Abstract

Let $F$ be a global field, and $G$ a connected reductive group defined over $F$. We prove that two endoscopic data of $G$ which are equivalent almost everywhere, are equivalent. The result remains true for (non-twisted) endoscopy with character. We also give, for $F$ global or local and $G$ quasi-simple simply connected, a description of the elliptic endoscopic data of $G$.