The integral Hodge conjecture for 3-folds of Kodaira dimension zero

Abstract

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.

21 pages

References in corpus (2)

• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero

Cited by in corpus (6)

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• Zero cycles on rationally connected varieties over Laurent fields
• Cylinder maps of algebraic cycles on cubic hypersurfaces