The Equivariant Tamagawa Number Conjecture for modular motives with   coefficients in Hecke algebras
  Under mild hypotheses on the residual representation, we prove the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras using a novel combination of the methods of Euler systems and Taylor-Wiles systems. We also prove the compatibility of this conjecture with specialization. 
Olivier Fouquet
math.NT