Iwasawa theory and zeta elements for \mathbbG_m

2015/06/26 by David Burns, Burns, David, Masato Kurihara +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1506.07935

openalex publication_date 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving special cases of the equivariant Tamagawa number conjecture. As a first application of this approach, we use it to prove new cases of the conjecture for Tate motives 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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