The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields

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 $\mu$-vanishing hypothesis is satisfied, also in the general case.