Modularity of PGL2(𝔽p)-representations over totally real fields.
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Peer-reviewed
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Abstract
We study an analog of Serre's modularity conjecture for projective representations [Formula: see text], where K is a totally real number field. We prove cases of this conjecture when [Formula: see text].
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Keywords
Galois representations, modular forms, number theory
Journal Title
Proc Natl Acad Sci U S A
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0027-8424
1091-6490
1091-6490
Volume Title
118
Publisher
Proceedings of the National Academy of Sciences
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All rights reserved
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European Research Council (714405)
P.A. was supported by Simons Foundation Collaboration Grant 527275 and NSF grant DMS-1902155. He would like to thank the third author and Cambridge University for hospitality during a visit where some of this work was completed. Parts of this work were completed while P.A. was a visitor at the Institute for Advanced Study, where he was partially supported by the NSF. He would like to thank the IAS for providing excellent working conditions during his stay. J.T.’s work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714405). This research was begun during the period that J.T. served as a Clay Research Fellow.