Langlands Base Change for GL(2)

TL;DR

This paper proves the existence of base change for classical newforms of odd level over totally real Galois number fields, under certain local conditions, extending the Langlands program for GL(2).

Contribution

It establishes new cases of Langlands base change for GL(2) over totally real Galois fields with minimal local assumptions.

Findings

Base change exists for all classical newforms of odd level over F/Q.

The proof works under simple local assumptions on F.

Extends Langlands correspondence to broader classes of fields.

Abstract

Let F be a totally real Galois number field. We prove the existence of base change relative to the extension F/Q for every classical newform of odd level, under simple local assumptions on the field F.