@article{5d7b903268c24a1b9b623c75432d0342,
title = "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 diffierent sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for GL2(AF ).",
keywords = "Galois representations, automorphic",
author = "Allen, {Patrick B.} and Frank Calegari and Ana Caraiani and Toby Gee and David Helm and {Le Hung}, {Bao V.} and James Newton and Peter Scholze and Richard Taylor and Thorne, {Jack A.}",
note = "Funding Information: B.L. was supported in part by NSF Grant DMS-1802037, NSF Grant DMS-1952678 and the Alfred P. Sloan Foundation. Funding Information: P.A. was supported in part by Simons Foundation Collaboration Grant for Mathematicians 527275, NSF Grant DMS-1902155, and by NSERC. Funding Information: 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. Funding Information: J.T. was supported by a Clay Research Fellowship and ERC Starting Grant 714405. Funding Information: R.T. was supported by NSF Grant DMS-1902265 during the revision of this paper. Funding Information: 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. Funding Information: J.N. was supported by a UKRI Future Leaders Fellowship grant MR/V021931/1. Funding Information: F.C. was supported in part by NSF Grants DMS-1701703 and DMS-2001097. Funding Information: P.S. was supported in part by a DFG Leibniz Grant, and by the DFG under the Excellence Strategy EXC-2047/1-390685813. Publisher Copyright: {\textcopyright} 2023 Department of Mathematics, Princeton University.",
year = "2023",
doi = "10.4007/ANNALS.2023.197.3.2",
language = "English (US)",
volume = "197",
pages = "897--1113",
journal = "Annals of Mathematics",
issn = "0003-486X",
publisher = "Princeton University Press",
number = "3",
}