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Potential automorphy over CM fields

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Allen, PB 
Calegari, F 
Caraiani, A 
Gee, T 
Helm, D 

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 poten- tially 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 ).

Description

Keywords

Galois representations, automorphic forms

Journal Title

Annals of Mathematics

Conference Name

Journal ISSN

0003-486X
1939-8980

Volume Title

Publisher

Annals of Mathematics
Sponsorship
European Research Council (714405)
P.A. was supported in part by Simons Foundation Collaboration Grant for Mathemati- cians 527275, NSF Grant DMS-1902155, and by NSERC. F.C. was supported in part by NSF Grants DMS-1701703 and DMS-2001097. A.C. was supported in part by NSF Grant DMS-1501064, by a Royal Society University Research Fellowship, by ERC Starting Grant 804176 and by a Leverhulme Prize. T.G. was supported in part by a Leverhulme Prize, EPSRC grant EP/L025485/1, ERC Starting Grant 306326, and a Royal Society Wolfson Research Merit Award. B.L. was supported in part by NSF Grant DMS-1802037, NSF Grant DMS-1952678 and the Alfred P. Sloan Foundation. J.N. was supported by a UKRI Future Leaders Fellowship, grant MR/V021931/1. P.S. was supported in part by a DFG Leibniz Grant, and by the DFG under the Excellence Strategy EXC-2047/1-390685813. R.T. was supported by NSF Grant DMS-1902265 during the revision of this paper. J.T. was supported by a Clay Research Fellowship and ERC Starting Grant 714405.