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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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Complex multiplication cycles and a conjecture of Beĭlinson and Bloch
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by Chad Schoen PDF
Trans. Amer. Math. Soc. 339 (1993), 87-115 Request permission

Abstract:

A generalization of the conjecture of Birch and Swinnerton-Dyer is investigated using complex multiplication cycles on a particular Kuga fiber variety. A weak finiteness result consistent with the conjecture is proved. The image of complex multiplication cycles under the Abel-Jacobi map is computed explicitly. The results provide numerical evidence supporting the conjecture. They also give evidence for a relationship between complex multiplication cycles and a modular form of weight $5/2$ and raise questions for further investigation.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 87-115
  • MSC: Primary 14C25; Secondary 11G40, 14G10, 14K22
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1107030-6
  • MathSciNet review: 1107030