The Hodge rings of abelian varieties associated to certain subsets of finite fields

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J. Math. Sci. Univ. Tokyo
Vol. 14 (2007), No. 1, Page 99--111.

HAZAMA, Fumio
The Hodge rings of abelian varieties associated to certain subsets of finite fields
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We construct a family of abelian varieties of CM-type such that the Hodge conjecture holds true for infinitely many members of it as well as their self-products. An intimate connection between the distribution of stably nondegenerate abelian varieties in the family and the coefficients of a certain modular form is revealed.

Mathematics Subject Classification (2000): 14C30, 14K22, 11G05.

Mathematical Reviews Number: MR2320386

Received: 2006-07-24

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