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2017 On Iwasawa theory, zeta elements for $\mathbb{G}_{m}$, and the equivariant Tamagawa number conjecture
David Burns, Masato Kurihara, Takamichi Sano
Algebra Number Theory 11(7): 1527-1571 (2017). DOI: 10.2140/ant.2017.11.1527

Abstract

We develop an explicit “higher-rank” Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of number fields. We show this theory leads to a concrete new strategy for proving special cases of the equivariant Tamagawa number conjecture and, as a first application of this approach, we prove new cases of the conjecture over natural families of abelian CM-extensions of totally real fields for which the relevant p-adic L-functions possess trivial zeroes.

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David Burns. Masato Kurihara. Takamichi Sano. "On Iwasawa theory, zeta elements for $\mathbb{G}_{m}$, and the equivariant Tamagawa number conjecture." Algebra Number Theory 11 (7) 1527 - 1571, 2017. https://doi.org/10.2140/ant.2017.11.1527

Information

Received: 3 May 2016; Revised: 1 March 2017; Accepted: 10 March 2017; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06775552
MathSciNet: MR3697147
Digital Object Identifier: 10.2140/ant.2017.11.1527

Subjects:
Primary: 11S40
Secondary: 11R23, 11R29, 11R42

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 7 • 2017
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