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On Iwasawa theory, zeta elements for Gm, and the equivariant Tamagawa number conjecture

Research output: Contribution to journalArticlepeer-review

David Burns, Masato Kurihara, Takamichi Sano

Original languageEnglish
Pages (from-to)1527-1571
Number of pages45
JournalAlgebra and Number Theory
Issue number7
Early online date7 Sep 2017
Accepted/In press10 Mar 2017
E-pub ahead of print7 Sep 2017
Published7 Sep 2017


King's Authors


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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