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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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A refined Beilinson–Bloch conjecture for motives of modular forms
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by Matteo Longo and Stefano Vigni PDF
Trans. Amer. Math. Soc. 369 (2017), 7301-7342 Request permission

Abstract:

We propose a refined version of the Beilinson–Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant $p$-adic Abel–Jacobi map to certain combinations of Heegner cycles on Kuga–Sato varieties. We prove theorems in the direction of the conjecture and, in doing so, obtain higher weight analogues of results for elliptic curves due to Darmon.
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Additional Information
  • Matteo Longo
  • Affiliation: Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy
  • MR Author ID: 790759
  • Email: mlongo@math.unipd.it
  • Stefano Vigni
  • Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
  • MR Author ID: 842395
  • Email: vigni@dima.unige.it
  • Received by editor(s): February 1, 2016
  • Published electronically: May 5, 2017
  • Additional Notes: The authors were partially supported by PRIN 2010–11 “Arithmetic Algebraic Geometry and Number Theory”. The first author was also partially supported by PRAT 2013 “Arithmetic of Varieties over Number Fields”. The second author was also partially supported by PRA 2013 “Geometria Algebrica e Teoria dei Numeri”.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 7301-7342
  • MSC (2010): Primary 14C25, 11F11
  • DOI: https://doi.org/10.1090/tran/6947
  • MathSciNet review: 3683110