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integral tate conjecture

Journal of the Institute of Mathematics of Jussieu (1)

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THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO
Part of
Burt Totaro
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 5 / September 2021

Published online by Cambridge University Press:

18 February 2020, pp. 1697-1717

Print publication:

September 2021
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We prove the integral Hodge conjecture for all 3-folds $X$ of Kodaira dimension zero with $H^{0}(X,K_{X})$ not zero. This generalizes earlier results of Voisin and Grabowski. The assumption is sharp, in view of counterexamples by Benoist and Ottem. We also prove similar results on the integral Tate conjecture. For example, the integral Tate conjecture holds for abelian 3-folds in any characteristic.