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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, 376. pp. 8095-8128. 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R006563/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Jun 2023 10:49 |
Last Modified: | 04 Oct 2024 14:04 |
Status: | Published |
Publisher: | American Mathematical Society |
Refereed: | Yes |
Identification Number: | 10.1090/tran/9001 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200100 |
Available Versions of this Item
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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]