Complex multiplication cycles and a conjecture of Beĭlinson and Bloch

Schoen, Chad

doi:10.1090/S0002-9947-1993-1107030-6

Complex multiplication cycles and a conjecture of Beĭlinson and Bloch
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by Chad Schoen

Trans. Amer. Math. Soc. 339 (1993), 87-115

DOI: https://doi.org/10.1090/S0002-9947-1993-1107030-6

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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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