Ordinary pseudorepresentations and modular forms

Author:

Wake Preston,Wang-Erickson Carl

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.

Publisher

American Mathematical Society (AMS)

Subject

General Medicine

Reference25 articles.

1. Families of Galois representations and Selmer groups;Bellaïche, Joël;Ast\'{e}risque,2009

2. Cambridge Studies in Advanced Mathematics;Bruns, Winfried,1993

3. Criteria for complete intersections;de Smit, Bart,1997

4. [FK12] Takako Fukaya and Kazuya Kato, On conjectures of Sharifi. Preprint, 2012.

5. Modular symbols in Iwasawa theory;Fukaya, Takako,2014

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On Density of Modular Points in Pseudo-Deformation Rings;International Mathematics Research Notices;2023-03-16

2. The universal ordinary deformation ring associated to a real quadratic field;Proceedings - Mathematical Sciences;2022-03-28

3. The Eisenstein ideal with squarefree level;Advances in Mathematics;2021-03

4. New criteria for Vandiver’s conjecture using Gauss sums – Heuristics and numerical experiments;Proceedings - Mathematical Sciences;2020-05-06

5. Pseudorepresentations of weight one are unramified;Algebra & Number Theory;2019-09-21

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3