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/ Q 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)), Z[Gal(L/K)]) .