On isomorphisms between deformation rings and Hecke rings

Abstract

We give a different approach to the well-known modularity lifting results of Wiles and Taylor. Instead of Taylor-Wiles systems we use a Galois cohomological discovery of R. Ramakrishna. This paper is 2 years older than math.NT/0210296 where another approach to modularity lifting results was presented.

References in corpus (1)

• Finiteness of Selmer groups and deformation rings

Cited by in corpus (13)

• On anticyclotomic mu-invariants of modular forms
• Indivisibility of Heegner points in the multiplicative case
• On Serre's reciprocity conjecture for 2-dimensional mod p representations of the Galois group of Q
• Finiteness of Selmer groups and deformation rings
• On Serre's modularity conjecture for 2-dimensional mod p representations of G_Q unramified outside p
• Horizontal variation of Tate--Shafarevich groups
• Quantitative level lowering for Galois representations
• On the quantitative variation of congruence ideals and integral periods of modular forms
• Automorphy of some residually S_5 Galois representations
• Wiles defect of Hecke algebras via local-global arguments
• Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory
• Wiles defect for Hecke algebras that are not complete intersections
• On maps between modular Jacobians and Jacobians of Shimura curves