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Hodge cycles on Kuga fiber varieties

Part of: Abelian varieties and schemes Cycles and subschemes

Published online by Cambridge University Press:  09 April 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics University of Northern IowaCedar Falls, Iowa 50614USA e-mail address: lee@math.uni.edu
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Abstract

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We determine the dimension of the space of Hodge cycles for the generic fibers of the Kuga fiber varieties associated to certain quaternion algebras.

MSC classification

Secondary: 14C30: Transcendental methods, Hodge theory , Hodge conjecture 14K10: Algebraic moduli, classification
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Abdulali, S., ‘Field of definition for some Hodge cycles’, Math. Ann. 285 (1989), 289–295.CrossRefGoogle Scholar
[2]Addington, S., ‘Equivariant holomorphic maps of symmetric domains’, Duke Math. J. 55 (1987), 65–88.CrossRefGoogle Scholar
[3]Gordon, B., ‘Topological and algebraic cycles in Kuga-Shimura varieties’, Math. Ann. 279 (1988), 395–402.CrossRefGoogle Scholar
[4]Kuga, M., Fiber varieties over a symmetric space whose fibers are abelian varieties I, II, Lecture Notes (Univ. of Chicago Press, Chicago, 1963/1964).Google Scholar
[5]Kuga, M., ‘Algebraic cycles in gtabv’, J. Fac. Sci. Univ. of Tokyo Sect. IA Math. 29 (1982), 13–29.Google Scholar
[6]Kuga, M., ‘Chemistry and GTABVs’, Progr. Math. 46 (1984), 269–281.Google Scholar
[7]Kuga, M., ‘Invariants and Hodge cycles’, Adv. Stud. Pure Math. 15 (1989), 373–413.CrossRefGoogle Scholar
[8]Lee, M. H., ‘Conjugates of equivariant holomorphic maps of symmetric domains’, Pacific J. Math. 149 (1991), 127–144.CrossRefGoogle Scholar
[9]Satake, I., Algebraic structures of symmetric domains (Princeton Univ. Press, Princeton, 1980).Google Scholar
[10]Tjiok, M. C., Algebraic cycles in a certain fiber variety (PhD. Thesis, SUNY at Stony Brook, 1980).Google Scholar