The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras

2016/04/21 by Olivier Fouquet, Fouquet, Olivier
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1604.06411

arxiv created 2016/04/21 · openalex publication_date 2016/04/21 · arxiv updated 2016/04/22 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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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