Potential automorphy over CM fields
File(s)1812.09999v1.pdf (1.59 MB)
Working paper
Author(s)
Type
Working Paper
Abstract
Let $F$ be a CM number field. We prove modularity lifting theorems for
regular $n$-dimensional Galois representations over $F$ without any
self-duality condition. We deduce that all elliptic curves $E$ over $F$ 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
$\mathrm{GL}_2(\mathbf{A}_F)$.
regular $n$-dimensional Galois representations over $F$ without any
self-duality condition. We deduce that all elliptic curves $E$ over $F$ 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
$\mathrm{GL}_2(\mathbf{A}_F)$.
Date Issued
2022-06-15
Citation
2022
Publisher
arXiv
Copyright Statement
© 2018 The Author(s)
Identifier
https://arxiv.org/abs/1812.09999v2
Subjects
math.NT
math.NT
Notes
192 pages
Publication Status
Accepted