On the integral Hodge conjecture for varieties with trivial Chow group

Abstract

We obtain examples of smooth projective varieties over $\mathbb{C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number fields.

arXiv commentsubmitted; comments welcome

References in corpus (4)

• Cohomologie non ramifiée et conjecture de Hodge entière
• Projectors on the intermediate algebraic Jacobians
• Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero
• A pencil of Enriques surfaces with non-algebraic integral Hodge classes

Cited by in corpus (1)

• On the failure of the integral Hodge/Tate conjecture for products with projective hypersurfaces