The equivariant Tamagawa Number Conjecture for abelian extensions of imaginary quadratic fields

2021/02/02 by Dominik Bullach, Bullach, Dominik, Martin Hofer +1
Mathematics · #11R42 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2102.01545

openalex publication_date 2021/02/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We prove the Iwasawa-theoretic version of a Conjecture of Mazur--Rubin and Sano in the case of elliptic units. This allows us to derive the p-part of the equivariant Tamagawa number conjecture at s = 0 for abelian extensions of imaginary quadratic fields in the semi-simple case and, provided that a standard μ-vanishing hypothesis is satisfied, also in the general case.

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