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arXiv · 2105.10975

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

Dominik Bullach·David Burns·Takamichi Sano
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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 Soul\'e 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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Dominik Bullach, David Burns, Takamichi Sano. 2021-05-23. On $p$-adic families of special elements for rank-one motives. https://arxiv.org/abs/2105.10975

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