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arXiv · 2112.04783

On the minus component of the equivariant Tamagawa number conjecture for $\mathbb{G}_m$

Mahiro Atsuta·Takenori Kataoka
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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 $\mathbb{G}_m$ 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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BibTeXRIS

Mahiro Atsuta, Takenori Kataoka. 2021-12-09. On the minus component of the equivariant Tamagawa number conjecture for $\mathbb{G}_m$. https://arxiv.org/abs/2112.04783

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