论文标题
Sur la susupure de tateentièrepour le produit d'une courbe et d'une表面$ ch_ {0} $ - triviale sur un corps fini
Sur la conjecture de Tate entière pour le produit d'une courbe et d'une surface $CH_{0}$-triviale sur un corps fini
论文作者
论文摘要
在假设表面在几何上是$ ch_0 $ - 平地的假设，我们研究了曲线和表面上的1循环的一体式泰特猜想的强大版本。我们的意思是，在任何代数封闭的场扩展上，表面的零维盘组上的度图是同构。这适用于Enriques表面。当Néron-Severi组没有扭转时，我们会恢复A. pirutka的早期结果。结果依赖于第三种特定品种特定产品的未遵循的共同研究小组的详细研究。
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 $CH_0$-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.
