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Hodge cycles and the Leray filtration

Hodge cycles and the Leray filtration

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 …