On the Chow groups of certain geometrically rational 5-folds

Ambrus Pal

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arXiv · 1207.4703

On the Chow groups of certain geometrically rational 5-folds

Ambrus Pal

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Abstract

We give an explicit regular model for the quadric fibration studied in Pirutka (2011). As an application we show that this construction furnishes a counterexample for the integral Tate conjecture in any odd characteristic for some sufficiently large finite field. We study the etale cohomology of this regular model, and as a consequence we derive that these counterexamples are not torsion.

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Ambrus Pal. 2012-07-19. On the Chow groups of certain geometrically rational 5-folds. https://arxiv.org/abs/1207.4703

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