Autour de la conjecture de Tate enti\`ere 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-Th\'el\`ene.

Keywords

• mathematics - algebraic geometry
• mathematics - number theory
• 14c25 (primary) 14c35, 14g15 (secondary)