Moduli Stacks of $G$-Curves in Homotopy Theory at $h=p-1$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918149780144128 |
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| author | Ray, Rin |
| author_facet | Ray, Rin |
| contents | We study the action on the deformation space of a formal group by the maximal finite subgroup $G$ of its automorphisms, at the first height where the group has nontrivial $p$-torsion for odd $p$. We show given this group $G$ there is a universal construction of a geometric model of the $G$-action via inverse Galois theory which generalizes the use of level structure to ramification data. We use configuration spaces to understand the model, and conclude that the Lubin-Tate action at $h=p-1$ is a subgroup of the symmetric group action on the configuration space of $p+1$ points on $\mathbb{P}^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli Stacks of $G$-Curves in Homotopy Theory at $h=p-1$ Ray, Rin Algebraic Geometry Algebraic Topology We study the action on the deformation space of a formal group by the maximal finite subgroup $G$ of its automorphisms, at the first height where the group has nontrivial $p$-torsion for odd $p$. We show given this group $G$ there is a universal construction of a geometric model of the $G$-action via inverse Galois theory which generalizes the use of level structure to ramification data. We use configuration spaces to understand the model, and conclude that the Lubin-Tate action at $h=p-1$ is a subgroup of the symmetric group action on the configuration space of $p+1$ points on $\mathbb{P}^1$. |
| title | Moduli Stacks of $G$-Curves in Homotopy Theory at $h=p-1$ |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2509.23428 |