Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

Let L/K be a nite Galois CM-extension of number elds with Galois group G. In an earlier paper, the author has de ned a module SKu(L/K) over the center of the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian and, in particular, contains many Stickelberger elements. It was shown that a certain conjecture on the integrality of SKu(L/K) implies the minus part of the equivariant Tamagawa number conjecture at an odd prime p for an in nite class of (non-abelian) Galois CM-extensions of number elds which are at most tamely rami ed above p, provided that Iwasawa's μ-invariant vanishes. Here, we prove a relevant part of this integrality conjecture which enables us to deduce the equivariant Tamagawa number conjecture from the vanishing of μ for the same class of extensions.