Wild euler systems of elliptic units and the Equivariant Tamagawa Number Conjecture

Let N/K be a finite abelian extension of a quadratic imaginary number field K. Let p denote a prime ideal in K of residue characteristic p such that p splits in K/Q and p splits completely in N/K. In analogy to a result of Solomon in the cyclotomic case we construct an elliptic p-unit in N and express its valuation in terms of a p-adic logarithm. As an application we prove the Equivariant Tamagawa Number Conjecture formulated by Bums and Flach for the pair (h(0)(Spec(N)), Z[Gal(N/K)]) for a natural family of genus extensions N/K.