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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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