2020/10/10 by Zhiyu Tian, Tian, Zhiyu
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2010.04996
openalex publication_date 2020/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study zero cycles on rationally connected varieties defined over characteristic zero Laurent fields with algebraically closed residue fields. We show that the degree map induces an isomorphism for rationally connected threefolds defined over such fields. In general, the degree map is an isomorphism if rationally connected varieties defined over algebraically closed fields of characteristic zero satisfy the integral Hodge/Tate conjecture for one cycles, or if the Tate conjecture is true for divisor classes on surfaces defined over finite fields. To prove these results, we introduce techniques from the minimal model program to study the homology of certain complexes defined by Kato/Bloch-Ogus.