Potential automorphy over CM fields
Number Theory
2022-06-17 v2
Abstract
Let be a CM number field. We prove modularity lifting theorems for regular -dimensional Galois representations over without any self-duality condition. We deduce that all elliptic curves over are potentially modular, and furthermore satisfy the Sato--Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for .
Cite
@article{arxiv.1812.09999,
title = {Potential automorphy over CM fields},
author = {Patrick B. Allen and Frank Calegari and Ana Caraiani and Toby Gee and David Helm and Bao V. Le Hung and James Newton and Peter Scholze and Richard Taylor and Jack A. Thorne},
journal= {arXiv preprint arXiv:1812.09999},
year = {2022}
}
Comments
A number of details have been included to address the concerns of the referees. The definition of decomposed generic (Def 4.3.1) has been weakened slightly to be in line with the current version of arxiv.org/abs/1909.01898, resulting in a strengthening of a number of our theorems. This is the accepted version of the paper