Sur la conjecture de Tate entière pour le produit d'une courbe et d'une surface $C{H}_0$-triviale sur un corps fini

Abstract

We investigate a strong version of the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field, under the assumption that the surface is geometrically $C{H}_0$-trivial. By this we mean that over any algebraically closed field extension, the degree map on the zero-dimensional Chow group of the surface is an isomorphism. This applies to Enriques surfaces. When the Néron-Severi group has no torsion, we recover earlier results of A. Pirutka. The results rely on a detailed study of the third unramified cohomology group of specific products of varieties.

33 pages, in French. Title changed (original title : Produit d'une courbe et d'une surface $C{H}_0$-triviale sur un corps fini : cohomologie non ramifiée et cycles de codimension deux). Introduction revised. New Remark 4.6

Cited by in corpus (1)

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