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

TY - JOUR

T1 - On p-adic families of special elements for rank-one motives

AU - Bullach, Dominik

AU - Burns, David

AU - Sano, Takamichi

PY - 2023/2/18

Y1 - 2023/2/18

N2 - 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 Soule 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.

AB - 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 Soule 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.

M3 - Article

SN - 0002-9947

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -