Potential Automorphy over CM Fields

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dc.contributor.authorThorne, Jack
dc.contributor.authorAllen, Patrick
dc.contributor.authorCalegari, Frank
dc.contributor.authorCaraiani, Ana
dc.contributor.authorGee, Toby
dc.contributor.authorHelm, David
dc.contributor.authorLe Hung, Bao V
dc.contributor.authorNewton, James
dc.contributor.authorScholze, Peter
dc.contributor.authorTaylor, Richard
dc.date.accessioned2022-06-30T23:30:06Z
dc.date.available2022-06-30T23:30:06Z
dc.identifier.issn0003-486X
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338643
dc.description.abstractLet 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 ).
dc.description.sponsorshipP.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.
dc.publisherMathematical Sciences Publishers (MSP)
dc.rightsAll Rights Reserved
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserved
dc.titlePotential Automorphy over CM Fields
dc.typeArticle
dc.publisher.departmentDepartment of Pure Mathematics And Mathematical Statistics
dc.date.updated2022-06-28T12:51:05Z
prism.publicationNameAnnals of Mathematics
dc.identifier.doi10.17863/CAM.86054
dcterms.dateAccepted2022-06-15
rioxxterms.versionAM
rioxxterms.typeJournal Article/Review
pubs.funder-project-idEuropean Research Council (714405)
cam.orpheus.counter20*
cam.depositDate2022-06-28
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement
rioxxterms.freetoread.startdate2025-06-30


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