Galois representations attached to automorphic forms on GL_2 over CM fields

TL;DR

This paper constructs compatible systems of Galois representations linked to automorphic forms on GL_2 over CM fields and proves a local-global compatibility result, extending previous work in the area.

Contribution

It generalizes Harris-Soudry-Taylor's work to CM fields and establishes local-global compatibility for these Galois representations.

Findings

Constructed compatible Galois systems for automorphic forms on GL_2 over CM fields.

Proved local-global compatibility up to semisimplification.

Extended previous results to a broader class of fields.

Abstract

In this paper we generalize the work of Harris-Soudry-Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on GL_2 over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semisimplification.