2020/01/28 by Jean-Louis Colliot-Thélène, Federico Scavia, Colliot-Thélène, Jean-Louis +1
Mathematics · #14C25 #14C35 #14G15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2001.10515
openalex publication_date 2020/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 CH0-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.