Hodge Cycles on Abelian Varieties with Complex Multiplication by Cyclic CM-Fields

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J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 4, Page 581--598.

Hazama, Fumio
Hodge Cycles on Abelian Varieties with Complex Multiplication by Cyclic CM-Fields
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Abstract:
For any cyclic CM-fields of degree $2pq$ with $p$, $q$ distinct odd primes, we determine which CM-types among $2^{pq}$ ones give rise to degenerate abelian varieties and in what codimension nondivisorial Hodge cycles exist on them.

Keywords: Hodge cycle, abelian variety, complex multiplication

Mathematics Subject Classification (1991): 14C30

Mathematical Reviews Number: MR2037760

Received: 2002-09-20

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