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Complex multiplication cycles and a conjecture of Beĭlinson and Bloch


Author: Chad Schoen
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1993-1107030-6
Article copyright: © Copyright 1993 American Mathematical Society

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