Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

Details Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

2011-08-04

arxiv.org/abs/1108.1062v1

Mathematics

Number Theory

17 pages

Scientific paper

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 equivariant Tamagawa number conjecture from the vanishing of $\mu$ for the same class of extensions.

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