On the minus component of the equivariant Tamagawa number conjecture for \mathbbG_m

2021/12/09 by Mahiro Atsuta, Atsuta, Mahiro, Takenori Kataoka +1
Mathematics · #11R29 #11R42 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2112.04783

openalex publication_date 2021/12/09 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

The equivariant Tamagawa number conjecture (hereinafter called the eTNC) predicts close relationships between algebraic and analytic aspects of motives. In this paper, we prove a lot of new cases of the minus component of the eTNC for \mathbbG_m and for CM abelian extensions. One of the main results states that the p-component of the eTNC is true when there exists at least one p-adic prime that is tamely ramified. The fundamental strategy is inspired by the work of Dasgupta and Kakde on the Brumer-Stark conjecture.

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