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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 Burns and Flach for the pair ( h  0 (Spec( N )), ℤ[Gal( N/K )]) for a natural family of genus extensions  N/K .

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