Ordinary pseudorepresentations and modular forms

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.

Final version, to appear in Proc. Amer. Math. Soc. 14 pages

References in corpus (1)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

Cited by in corpus (5)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• The Eisenstein ideal with squarefree level
• Deformation conditions for pseudorepresentations
• Test of Vandiver's conjecture with Gauss sums -- Heuristics
• Galois deformation rings and modularity in the residually reducible case