2022/11/29 by Zhiyu Tian, Tian, Zhiyu
Arts and Humanities · Mathematics · #14C25 #14G12 #14G25 #14M22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #North African History and Literature
paper · pdf · doi:10.48550/arxiv.2211.15915
openalex publication_date 2022/11/29 · openalex created_date 2022/12/11 · openalex updated_date 2026/07/28
We give a geometric criterion to check the validity of the integral Tate conjecture for one-cycles on a smooth projective variety that is separably rationally connected in codimension one, and to check that the Brauer-Manin obstruction is the only obstruction to the local-global principle for zero-cycles on a separably rationally connected variety defined over a global function field. We prove that the Brauer-Manin obstruction is the only obstruction to the local-global principle for zero-cycles on all geometrically rational surfaces defined over a global function field, and to the Hasse principle for rational points on del Pezzo surfaces of degree four defined over a global function field of odd characteristic. Along the way, we also prove some results about the space of one-cycles on a smooth projective variety that is separably rationally connected in codimension one, which leads to the equality of the coniveau filtration and the strong coniveau filtration on degree 3 homology of such varieties.