$$\mathbb {A}^1$$ A 1 -connected varieties of rank one over nonclosed fields
$$\mathbb {A}^1$$ A 1 -connected varieties of rank one over nonclosed fields
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$$mathbb {A}^1$$ 非闭域上的一阶 1 连通簇
DOI：
10.1007/s00208-015-1257-1
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发表时间：
2016
影响因子：
1.4
通讯作者：
Zhu, Yi
中科院分区：
文献类型：
--
作者：
Chen, Qile;Zhu, Yi
本文证明了秩为1的可分连通簇的算术的两个结果。首先证明了在大域上，如果边界因子光滑且可分离有理连通，则存在一条通过边界的任意有理点的曲线。其次，推广了Hassett-Tschinkel关于曲线函数域上整点的Zurski稠密性的一个定理。
In this paper, we prove two results regarding the arithmetics of separably-connected varieties of rank one. First we prove that 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.