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Potential automorphy over CM fields

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 GL2(AF ).
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4007/annals.2023.197.3.2

Authors


Publisher:
Princeton University Press
Journal:
Annals of Mathematics More from this journal
Volume:
197
Pages:
897-1113
Publication date:
2023-03-23
Acceptance date:
2022-06-15
DOI:
ISSN:
0003-486X
Language:
English
Keywords:
Pubs id:
1263827
Local pid:
pubs:1263827
Deposit date:
2022-06-15

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