Vol. 319, No. 2, 2022

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Hodge cycles and the Leray filtration

Donu Arapura

Vol. 319 (2022), No. 2, 233–258

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.

Hodge cycles, elliptic surfaces, Shimura curves
Mathematical Subject Classification
Primary: 14C30
Received: 4 July 2021
Revised: 13 June 2022
Accepted: 25 June 2022
Published: 11 September 2022
Donu Arapura
Department of Mathematics
Purdue University
West Lafayette, IN
United States