Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Topology on Points on Stacks   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.

34
The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph