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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


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Volume 2016, Issue 719

Issues

Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

Andreas Nickel
Published Online: 2014-06-18 | DOI: https://doi.org/10.1515/crelle-2014-0042

Abstract

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 G 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 μ-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 μ 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 provided that certain μ-invariants vanish.

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About the article

Received: 2012-10-30

Revised: 2014-04-04

Published Online: 2014-06-18

Published in Print: 2016-10-01


The author acknowledges financial support provided by the DFG.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 719, Pages 101–132, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0042.

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