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Proceedings of the American Mathematical Society Series B

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Ordinary pseudorepresentations and modular forms


Authors: Preston Wake and Carl Wang-Erickson
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
Published electronically: December 18, 2017
MathSciNet review: 3738092
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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.


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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
Article copyright: © Copyright 2017 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)