Potential automorphy over CM fields
File(s)
Accepted version
Author(s)
Type
Journal Article
Abstract
Let F be a CM number field. We prove modularity lifting theorems
for regular n-dimensional Galois representations over F without any selfduality 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 GL2(AF ).
for regular n-dimensional Galois representations over F without any selfduality 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 GL2(AF ).
Date Issued
2023-05
Date Acceptance
2023-05-01
Citation
Annals of Mathematics, 2023, 197 (3), pp.897-1113
ISSN
0003-486X
Publisher
Princeton University
Start Page
897
End Page
1113
Journal / Book Title
Annals of Mathematics
Volume
197
Issue
3
Copyright Statement
Copyright © 2023 The Author(s)
Identifier
https://arxiv.org/abs/1812.09999
Subjects
ADMISSIBLE REPRESENTATIONS
automorphic forms
CLASSIFICATION
COHOMOLOGY
EULER PRODUCTS
Galois representations
Mathematics
ORDINARY PARTS
Physical Sciences
PSEUDOREPRESENTATIONS
Science & Technology
Publication Status
Published
Date Publish Online
2023-05