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Berger, T. orcid.org/0000-0002-5207-6221 and Klosin, K. (2023) R=T theorems for weight one modular forms. Transactions of the American Mathematical Society. ISSN 0002-9947
Abstract
We prove modularity of certain residually reducible ordinary 2- dimensional p-adic Galois representations with determinant a finite order odd character χ. For certain non-quadratic χ we prove an R = T result for T the weight 1 specialisation of the cuspidal Hida Hecke algebra acting on nonclassical weight 1 forms. Under the additional assumption that no two cuspidal Hida families congruent to an Eisenstein series cross in weight 1 we show that T is reduced. For quadratic χ we prove that the quotient of R corresponding to deformations split at p is isomorphic to the Hecke algebra acting on classical CM weight 1 modular forms.
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Copyright, Publisher and Additional Information: | © 2023 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in Transactions of the American Mathematical Society is made available under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ | ||||
Keywords: | 11F33; 11F80; math.NT; math.NT | ||||
Dates: |
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) | ||||
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 15 Jun 2023 10:49 | ||||
Last Modified: | 07 Sep 2023 08:38 | ||||
Status: | Published online | ||||
Publisher: | American Mathematical Society | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.1090/tran/9001 | ||||
Related URLs: |
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R=T theorems for weight one modular forms. (deposited 07 Jun 2023 13:01)
- R=T theorems for weight one modular forms. (deposited 15 Jun 2023 10:49) [Currently Displayed]