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.References
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Bibliographic Information
- Dominik Bullach
- Affiliation: King’s College London, Department of Mathematics, London WC2R 2LS, United Kingdom
- ORCID: 0000-0002-3041-3282
- Email: dominik.bullach@kcl.ac.uk
- David Burns
- Affiliation: King’s College London, Department of Mathematics, London WC2R 2LS, United Kingdom
- MR Author ID: 43610
- Email: david.burns@kcl.ac.uk
- Takamichi Sano
- Affiliation: Osaka Metropolitan University, Department of Mathematics, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- ORCID: 0000-0002-6991-667X
- Email: tsano@omu.ac.jp
- Received by editor(s): September 24, 2021
- Received by editor(s) in revised form: October 3, 2022
- Published electronically: May 19, 2023
- Additional Notes: The first author was financially supported by the Engineering and Physical Sciences Research Council [EP/L015234/1], the EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London and King’s College London
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 5377-5407
- MSC (2020): Primary 11G40, 11R23
- DOI: https://doi.org/10.1090/tran/8929
- MathSciNet review: 4630748