Autour de la conjecture de Tate entière pour certains produits de dimension $3$ sur un corps fini

Abstract

Let $X$ be the product of a surface satisfying $b_2=\rho$ and of a curve over a finite field. We study a strong form of the integral Tate conjecture for $1$-cycles on $X$. We generalize and give unconditional proofs of several results of our previous paper with J.-L. Colliot-Thélène.

in French. Improves on the results of arXiv:2001.10515. Final version

References in corpus (2)

• The integral Hodge conjecture for 3-folds of Kodaira dimension zero
• Sur la conjecture de Tate entière pour le produit d'une courbe et d'une surface $C{H}_0$-triviale sur un corps fini