Ordinary pseudorepresentations and modular forms
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- by Preston Wake and Carl Wang-Erickson HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 4 (2017), 53-71
Abstract:
In this note, we observe that the techniques of our paper “Pseudo-modularity and Iwasawa theory” can be used to provide a new proof of some of the residually reducible modularity lifting results of Skinner and Wiles. In these cases, we have found that a deformation ring of ordinary pseudorepresentations is equal to the Eisenstein local component of a Hida Hecke algebra. We also show that Vandiver’s conjecture implies Sharifi’s conjecture.References
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Additional Information
- Preston Wake
- Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
- MR Author ID: 1098592
- Email: wake@math.ucla.edu
- Carl Wang-Erickson
- Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
- MR Author ID: 818082
- ORCID: 0000-0002-1230-7574
- Email: c.wang-erickson@imperial.ac.uk
- Received by editor(s): October 7, 2015
- Received by editor(s) in revised form: October 17, 2015, November 28, 2015, July 10, 2016, December 16, 2016, and January 13, 2017
- Published electronically: December 18, 2017
- Communicated by: Romyar T. Sharifi
- © Copyright 2017 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 4 (2017), 53-71
- MSC (2010): Primary 11F33, 11F80, 11R23
- DOI: https://doi.org/10.1090/bproc/29
- MathSciNet review: 3738092