On 𝑝-adic families of special elements for rank-one motives

Bullach, Dominik; Burns, David; Sano, Takamichi

doi:10.1090/tran/8929

On $p$-adic families of special elements for rank-one motives
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by Dominik Bullach, David Burns and Takamichi Sano

Trans. Amer. Math. Soc. 376 (2023), 5377-5407

DOI: https://doi.org/10.1090/tran/8929

Published electronically: May 19, 2023

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Abstract:

We conjecture that special elements associated with rank-one motives are obtained $p$-adically from Rubin–Stark elements by means of a precise higher-rank Soulé twist construction. We show this conjecture incorporates a variety of known results and existing predictions and also gives rise to a concrete strategy for proving the equivariant Tamagawa Number Conjecture for rank-one motives. We then use this approach to obtain new evidence in support of the equivariant Tamagawa Number Conjecture in the setting of CM abelian varieties.

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