论文标题
良好的还原和循环盖
Good reduction and cyclic covers
论文作者
论文摘要
我们证明了在数字字段上的一组品种的有限结果，并在给定有限的地方使用循环盖子进行了良好的降低。我们获得了Shafarevich猜想的版本，用于加权的投影表面，Abelian品种的双重覆盖物，并将Hypersurfaces的Shafarevich猜想减少到高度高尺寸的高度外面。这些是在循环盖模量堆栈上积分点的一般设置的特殊情况，我们的算术结果是通过Chevalley-Weil定理的版本来实现的。
We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double covers of abelian varieties, and reduce the Shafarevich conjecture for hypersurfaces to the case of hypersurfaces of high dimension. These are special cases of a general set-up for integral points on moduli stacks of cyclic covers, and our arithmetic results are achieved via a version of the Chevalley-Weil theorem for stacks.
