Modularity of PGL(2)(F-p)-representations over totally real fields

Modularity of PGL(2)(F-p)-representations over totally real fields

We study an analog of Serre's modularity conjecture for projective representations (rho) over bar: Gal((K) over bar /K) -> PGL(2)(k), where K is a totally real number field. We prove cases of this conjecture when k = F-5.

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Veröffentlicht in:Proceedings of the National Academy of Sciences - PNAS 2021-08, Vol.118 (33), Article 2108064118
Hauptverfasser: Allen, Patrick B., Khare, Chandrashekhar B., Thorne, Jack A.
Format: Artikel
Sprache:eng
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Multidisciplinary Sciences
Science & Technology
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Zusammenfassung:We study an analog of Serre's modularity conjecture for projective representations (rho) over bar: Gal((K) over bar /K) -> PGL(2)(k), where K is a totally real number field. We prove cases of this conjecture when k = F-5.
ISSN:0027-8424
DOI:10.1073/pnas.2108064118