Local structure of smooth \texorpdfstring{$p$}{p}-adic analytic Artin stacks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915825614585856 |
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| author | Kaminski, Amos |
| author_facet | Kaminski, Amos |
| contents | We prove \cite[Conjecture~5.17]{Clausen} on the local light--profinite structure of smooth $p$-adic analytic Artin stacks. The argument proceeds in several reductions. First, by proving a generalization of van~Dantzig theorem for groupoids, we reduce the conjecture to the compact Hausdorff case. This reduces the conjecture to the statement that the geometric realization of a groupoid object whose object and morphism spaces are light profinite and whose source and target maps are open is light profinite. Next, we simplify the groupoid by constructing a closed skeleton; after quotienting by a clopen subgroupoid, the remaining problem reduces to proving that a profinite family of finite groups can be presented as an inverse limit of finite families of finite groups. As observed by Clausen immediately after \cite[Conjecture~5.17]{Clausen}, our result implies in particular that smooth $p$-adic analytic Artin stacks are \emph{$!$-good}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00733 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local structure of smooth \texorpdfstring{$p$}{p}-adic analytic Artin stacks Kaminski, Amos Algebraic Topology Algebraic Geometry We prove \cite[Conjecture~5.17]{Clausen} on the local light--profinite structure of smooth $p$-adic analytic Artin stacks. The argument proceeds in several reductions. First, by proving a generalization of van~Dantzig theorem for groupoids, we reduce the conjecture to the compact Hausdorff case. This reduces the conjecture to the statement that the geometric realization of a groupoid object whose object and morphism spaces are light profinite and whose source and target maps are open is light profinite. Next, we simplify the groupoid by constructing a closed skeleton; after quotienting by a clopen subgroupoid, the remaining problem reduces to proving that a profinite family of finite groups can be presented as an inverse limit of finite families of finite groups. As observed by Clausen immediately after \cite[Conjecture~5.17]{Clausen}, our result implies in particular that smooth $p$-adic analytic Artin stacks are \emph{$!$-good}. |
| title | Local structure of smooth \texorpdfstring{$p$}{p}-adic analytic Artin stacks |
| topic | Algebraic Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2603.00733 |