On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field

  • W. Bley

    Universität Kassel Fachbereich 17 D-34109 Kassel Germany
On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field cover
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Abstract

Let kk be a quadratic imaginary field, pp a prime which splits in k/\Quk/\Qu and does not divide the class number hkh_k of kk. Let LL denote a finite abelian extension of kk and let KK be a subextension of L/kL/k. In this article we prove the pp-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(\Spec(L)),\Ze[\Gal(L/K)])(h^0(\Spec(L)), \Ze[\Gal(L/K)]).

Cite this article

W. Bley, On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field. Doc. Math. 11 (2006), pp. 73–118

DOI 10.4171/DM/205