Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

Nickel A. Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. 2016;719(719):101-132.Let L / K be a finite Galois CM-extension of number fields with Galois group G. In an earlier paper, the author has defined 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 infinite class of (non-abelian) Galois CM-extensions of number fields which are at most tamely ramified above p, provided that Iwasawa's mu-invariant vanishes. Here, we prove a relevant part of this integrality conjecture which enables us to deduce the minus-p-part of the equivariant Tamagawa number conjecture from the vanishing of mu for the same class of extensions. As an application we prove the non-abelian Brumer and Brumer-Stark conjecture outside the 2-primary part for every monomial Galois extension of Q provided that certain mu-invariants vanish