2017/10/09 by Jean-Louis Colliot-Thélène, Colliot-Thélène, Jean-Louis, David Harbater +9
Computer Science · Mathematics · #14C25 #14G05 #14H25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C25 #msc:14G05 #msc:14H25
paper · pdf · doi:10.48550/arxiv.1710.03173
23 pages. Some explanations were expanded for greater clarity throughout the paper. Some results in Section 2 in the earlier version in the complete case were generalized here to the henselian case. Subsection 3.3 in the earlier version was broken into two subsections, and there was some renumbering of results in the new Subsection 3.4 due to an added remark
openalex publication_date 2017/10/09 · openalex created_date 2017/10/20 · arxiv created 2018/04/15 · arxiv updated 2018/04/17 · openalex updated_date 2026/07/28
We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show that local-global principles hold for such zero-cycles provided that local-global principles hold for the existence of rational points over extensions of the function field. This assertion is analogous to a known result concerning varieties over number fields. We also show that our results hold more generally in the henselian case.