论文标题
二叠纪曲线上积分点的本地全球原理
The local-global principle for integral points on stacky curves
论文作者
论文摘要
我们在$ \ Mathbb {z} $上构建了$ 1/2 $（即Euler特征$ 1 $）的繁琐曲线，该曲线具有$ \ MATHBB {r} $ - 点和$ \ Mathbb {z} _p $ - 点的$ \ point $ p $ p $，但没有$ \ mathbb {z} $ - 点。最好的可能是：我们还证明，在全球田地的$ s $ ingers上，任何属于$ 1/2 $的二叠纪曲线都可以满足整体积分的本地全球原则。
We construct a stacky curve of genus $1/2$ (i.e., Euler characteristic $1$) over $\mathbb{Z}$ that has an $\mathbb{R}$-point and a $\mathbb{Z}_p$-point for every prime $p$ but no $\mathbb{Z}$-point. This is best possible: we also prove that any stacky curve of genus less than $1/2$ over a ring of $S$-integers of a global field satisfies the local-global principle for integral points.
