On the geometry of integral models of Shimura varieties with $Γ_1(p)$-level structure
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918160470376448 |
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| author | Marazza, Giulio |
| author_facet | Marazza, Giulio |
| contents | We study integral models of some Shimura varieties with bad reduction at a prime $p$, namely the Siegel modular variety and Shimura varieties associated with some unitary groups. We focus on the case where the level structure at $p$ is given by the pro-unipotent radical of an Iwahori subgroup, and we analyze the geometry of the integral models that have been proposed until now: we show that they are almost never normal and in some cases not flat over $\mathbb{Z}_p$. We do so by showing the failure of these geometric properties on the corresponding local models, and we explain how the local model diagrams can be interpreted using the root stack construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometry of integral models of Shimura varieties with $Γ_1(p)$-level structure Marazza, Giulio Algebraic Geometry primary 11G18, secondary 14G35 We study integral models of some Shimura varieties with bad reduction at a prime $p$, namely the Siegel modular variety and Shimura varieties associated with some unitary groups. We focus on the case where the level structure at $p$ is given by the pro-unipotent radical of an Iwahori subgroup, and we analyze the geometry of the integral models that have been proposed until now: we show that they are almost never normal and in some cases not flat over $\mathbb{Z}_p$. We do so by showing the failure of these geometric properties on the corresponding local models, and we explain how the local model diagrams can be interpreted using the root stack construction. |
| title | On the geometry of integral models of Shimura varieties with $Γ_1(p)$-level structure |
| topic | Algebraic Geometry primary 11G18, secondary 14G35 |
| url | https://arxiv.org/abs/2509.21198 |