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THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO

Part of: Surfaces and higher-dimensional varieties (Co)homology theory Cycles and subschemes

Published online by Cambridge University Press:  18 February 2020

Burt Totaro Open the ORCID record for Burt Totaro [Opens in a new window]
Burt Totaro*
Affiliation:
UCLA, Department of Mathematics, Los Angeles, CA, USA ([email protected])
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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.

Keywords

integral Hodge conjectureintegral Tate conjecture3-foldCalabi–Yau manifold

MSC classification

Primary: 14C30: Transcendental methods, Hodge theory , Hodge conjecture
Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 14J30: $3$-folds 14J32: Calabi-Yau manifolds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 5 , September 2021 , pp. 1697 - 1717
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Copyright
© Cambridge University Press 2020

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