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Complex Multiplication Cycles and a Conjecture of Beilinson and Bloch

Chad Schoen
Transactions of the American Mathematical Society
Vol. 339, No. 1 (Sep., 1993), pp. 87-115
DOI: 10.2307/2154210
Stable URL: http://www.jstor.org/stable/2154210
Page Count: 29
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Complex Multiplication Cycles and a Conjecture of Beilinson and Bloch
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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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