Generalizes Iwasawa invariant behavior under congruences and establishes propagation of Kato's main conjecture for higher weight modular forms at good primes assuming mod p non-vanishing of zeta elements.
The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras
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abstract
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.
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2019 1verdicts
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On the Iwasawa invariants of Kato's zeta elements for modular forms
Generalizes Iwasawa invariant behavior under congruences and establishes propagation of Kato's main conjecture for higher weight modular forms at good primes assuming mod p non-vanishing of zeta elements.