Caract\`eres automorphes d'un groupe r\'eductif

TL;DR

This paper proves that a specific homomorphism from a cohomology group of the center of the dual group to automorphic characters of a reductive group over a number field is bijective, clarifying a key aspect of Langlands' conjectures.

Contribution

It establishes the bijectivity of a homomorphism defined by Langlands from a cohomology group to automorphic characters for reductive groups over number fields.

Findings

Proves bijectivity of Langlands' homomorphism.

Clarifies the structure of automorphic characters.

Enhances understanding of the Langlands correspondence.

Abstract

Let $G$ be a reductive group defined over a number field. Denote $Z(\hat G)$ the center of the dual group. Langlands has defined some homomorphism from some cohomology group of $Z(\hat G)$ into the group of automorphic characters of $G$. We prove that it is bijective.