On the Equivariant Tamagawa Number Conjecture for Abelian Extensions of a Quadratic Imaginary Field

Let $k$ be a quadratic imaginary field, $p$ a prime which splits in $k/\Qu$ and does not divide the class number $h_k$ of $k$. Let $L$ denote a finite abelian extension of $k$ and let $K$ be a subextension of $L/k$. In this article we prove the $p$-part of the Equivariant Tamagawa Number Conjecture for the pair $(h^0(\Spec(L)), \Ze[\Gal(L/K)])$.

2000 Mathematics Subject Classification: 11G40, 11R23, 11R33, 11R65

Keywords and Phrases: L-functions, Iwasawa theory, Euler systems

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