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

2021/05/23 by Bullach, Dominik, Burns, David, Sano, Takamichi
#11S40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2105.10975

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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