Ordinary pseudorepresentations and modular forms
File(s)
Published version
Author(s)
Wake, P
Wang-Erickson, C
Type
Journal Article
Abstract
In this short note, we observe that the techniques of our recent work
"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.
"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.
Editor(s)
Sharifi, Romyar
Date Issued
2017-12-18
Date Acceptance
2017-01-15
Citation
Proceedings of the American Mathematical Society, Series B, 2017, 4, pp.53-71
ISSN
2330-1511
Publisher
American Mathematical Society
Start Page
53
End Page
71
Journal / Book Title
Proceedings of the American Mathematical Society, Series B
Volume
4
Copyright Statement
© Copyright 2017 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
License URL
Identifier
http://www.ams.org/journals/bproc/2017-04-06/S2330-1511-2017-00029-4/
Subjects
11F33, 11F80, 11R23
math.NT
Notes
18 pages; expositional improvements and fixed proof of Theorem 5.2.3
Publication Status
Published
Date Publish Online
2017-12-18