Potentially diagonalizable modular lifts of large weight
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/60129DOI: 10.1016/j.jnt.2021.03.023
ISSN: 0022-314X
Publisher
Elsevier
Date
2021-11-01Funders
Agencia Estatal de Investigación
Bibliographic citation
Blanco Chacón, I. & Dieulefait, L. 2021, “Potentially diagonalizable modular lifts of large weight”, Journal of Number Theory, vol. 228, pp. 188-207.
Keywords
Potential automorphy
Potentially diagonalizable representations
Potential modularity
Langlands functoriality
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-79400-P/ES/SIMETRIAS EN GEOMETRIA ARITMETICA, ALGEBRAICA Y SIMPLECTICA/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.jnt.2021.03.023Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
© 2021 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
We prove that for a Hecke cuspform f ∈ Sk(Γ0(N), χ) and a
prime l > max{k, 6} such that l ∤ N, there exists an infinite family {kr}r≥1 ⊆ Z
such that for each kr, there is a cusp form fkr ∈ Skr
(Γ0(N), χ) such that the
Deligne representation ρfkr,l is a crystalline and potentially diagonalizable lift
of ρf,l . When f is l-ordinary, we base our proof on the theory of Hida families,
while in the non-ordinary case, we adapt a local-to-global argument due to
Khare and Wintenberger in the setting of their proof of Serre’s modularity
conjecture, together with a result on existence of lifts with prescribed local
conditions over CM fields, a flatness result due to Böckle and a local dimension
result by Kisin. We discuss the motivation and tentative future applications of
our result in ongoing research on the automorphy of GL2n-type representations
in the higher level case.
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