$\mathbb{A}^1$-connected varieties over non-closed fields
Algebraic Geometry
2016-10-04 v2 Number Theory
Abstract
In this paper, we proved two results regarding the arithmetics of separably -connected varieties of rank one. First we proved over a large field, there is an -curve through any rational point of the boundary, if the boundary divisor is smooth and separably rationally connected. Secondly, we generalize a theorem of Hassett-Tschinkel for the Zariski density of integral points over function fields of curves.
Cite
@article{arxiv.1409.6398,
title = {$\mathbb{A}^1$-connected varieties over non-closed fields},
author = {Qile Chen and Yi Zhu},
journal= {arXiv preprint arXiv:1409.6398},
year = {2016}
}
Comments
11 pages; final version; to appear in Mathematische Annalen