Sur les donn{\'e}es endoscopiques dans le cas de l'endoscopie tordue

TL;DR

This paper provides a combinatorial description of elliptic endoscopic data for twisted spaces under semi-simple, simply connected groups, and proves their local-global equivalence over number fields.

Contribution

It introduces a simple combinatorial framework for elliptic endoscopic data and establishes a local-global equivalence result over number fields.

Findings

Provides a combinatorial description of elliptic endoscopic data.

Proves that local equivalence implies global equivalence for elliptic endoscopic data.

Applicable to semi-simple, simply connected groups over number fields.

Abstract

We give a simple combinatorial description of the elliptic endoscopic data of a twisted space under a group $G$, assuming that $G$ is semi-simple and simply connected. Assuming the same hypothesis and that the base field is a number field, we prove that, if two elliptic endoscopic data are equivalent almost everywhere, then they are equivalent.