论文标题
堆栈点的拓扑
A Topology on Points on Stacks
论文作者
论文摘要
对于某些拓扑环$ r $的品种，例如$ \ mathbb {z} _p $或$ \ mathbb {c} $，有一种很好的方法来拓展该品种上的$ r $ points。在本文中，我们将此定义推广到代数堆栈。对于许多拓扑环$ r $上的代数堆栈$ \ mathfrak {x} $，我们在$ r $ points $ \ mathfrak {x} $的同构类别上定义了拓扑。我们证明了所得拓扑空间的预期性能，包括功能。然后，我们将定义扩展到$ r $是某些全球字段的Adele的圈时的情况。最后，我们使用这个最后一个定义来增强Bhargava的堆栈曲线的局部全球兼容性，以达到强近似结果。
For a variety over certain topological rings $R$, like $\mathbb{Z}_p$ or $\mathbb{C}$, there is a well-studied way to topologize the $R$-points on the variety. In this paper, we generalize this definition to algebraic stacks. For an algebraic stack $\mathfrak{X}$ over many topological rings $R$, we define a topology on the isomorphism classes of $R$-points of $\mathfrak{X}$. We prove expected properties of the resulting topological spaces including functoriality. Then, we extend the definition to the case when $R$ is the ring of adeles of some global field. Finally, we use this last definition to strengthen the local-global compatibility for stacky curves of Bhargava--Poonen to a strong approximation result.
