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Abstract
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Given a fibered variety, we pull back the Leray filtration to the Chow group,
and use this to give some criteria for the Hodge and Tate conjectures to
hold for such varieties. We show that the Hodge conjecture holds for a good
desingularization of a self fibre product of a nonisotrivial elliptic surface under
appropriate conditions. We also show that the Hodge and Tate conjectures hold for
natural families of abelian varieties parametrized by certain Shimura curves.
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Keywords
Hodge cycles, elliptic surfaces, Shimura curves
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Mathematical Subject Classification
Primary: 14C30
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Milestones
Received: 4 July 2021
Revised: 13 June 2022
Accepted: 25 June 2022
Published: 11 September 2022
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