Pseudo-modularity and Iwasawa theory

Abstract

We prove, assuming Greenberg's conjecture, that the ordinary eigencurve is Gorenstein at an intersection point between the Eisenstein family and the cuspidal locus. As a corollary, we obtain new results on Sharifi's conjecture. This result is achieved by constructing a universal ordinary pseudodeformation ring and proving an $R=\mathbb{T}$ result.

Changes to section 5.9; typos corrected. To appear in Amer. J. Math. 54 pages

References in corpus (2)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• Companion forms and the structure of p-adic Hecke algebras

Cited by in corpus (9)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• The Eisenstein ideal with squarefree level
• The rank of Mazur's Eisenstein ideal
• Class groups and local indecomposability for non-CM forms
• Deformation conditions for pseudorepresentations
• Test of Vandiver's conjecture with Gauss sums -- Heuristics
• Explicit non-Gorenstein R=T via rank bounds I: Deformation theory
• On Sharifi's conjecture: exceptional case
• Critical Lambda-adic modular forms and bi-ordinary complexes