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

David Burns, Masato Kurihara, Takamichi Sano

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)1527-1571
Number of pages45
JournalAlgebra and Number Theory
Volume11
Issue number7
DOIs
Publication statusPublished - 2017

Keywords

  • Equivariant tamagawa number conjecture
  • Higher-rank iwasawa main conjecture
  • Rubin-stark conjecture

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On Iwasawa theory, zeta elements for G<sub>m</sub>, and the equivariant Tamagawa number conjecture'. Together they form a unique fingerprint.

Cite this