Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture

Nickel A (2016)
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 719(719): 101-132.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Erscheinungsjahr
2016
Zeitschriftentitel
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Band
719
Ausgabe
719
Seite(n)
101-132
ISSN
0075-4102
eISSN
1435-5345
Page URI
https://pub.uni-bielefeld.de/record/2906724

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Nickel A. Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. 2016;719(719):101-132.
Nickel, A. (2016). Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 719(719), 101-132. doi:10.1515/crelle-2014-0042
Nickel, A. (2016). Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 719, 101-132.
Nickel, A., 2016. Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 719(719), p 101-132.
A. Nickel, “Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture”, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, vol. 719, 2016, pp. 101-132.
Nickel, A.: Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. 719, 101-132 (2016).
Nickel, Andreas. “Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture”. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 719.719 (2016): 101-132.

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