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

## TL;DR

This paper proves the integral Hodge conjecture for certain 3-folds of Kodaira dimension zero and extends results to the integral Tate conjecture, including abelian 3-folds in any characteristic.

## Contribution

It establishes the integral Hodge conjecture for all 3-folds of Kodaira dimension zero with non-zero canonical sections, generalizing prior work and confirming sharpness of assumptions.

## Key findings

- Proves the integral Hodge conjecture for 3-folds of Kodaira dimension zero.
- Extends results to the integral Tate conjecture for abelian 3-folds.
- Confirms the sharpness of the assumptions with counterexamples.

## 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.