Canonical integral models for Shimura varieties of toral type
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912217941671936 |
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| author | Daniels, Patrick |
| author_facet | Daniels, Patrick |
| contents | We prove the Pappas-Rapoport conjecture on the existence of canonical integral models of Shimura varieties with parahoric level structure in the case where the Shimura variety is defined by a torus. As an important ingredient, we show, using the Bhatt-Scholze theory of prismatic $F$-crystals, that there is a fully faithful functor from $\mathcal{G}$-valued crystalline representations of Gal$(\bar{K}/K)$ to $\mathcal{G}$-shtukas over Spd$(\mathcal{O}_K)$, where $\mathcal{G}$ is a parahoric group scheme over $\mathbb{Z}_p$ and $\mathcal{O}_K$ is the ring of integers in a $p$-adic field $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09513 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Canonical integral models for Shimura varieties of toral type Daniels, Patrick Number Theory Algebraic Geometry 11G18 We prove the Pappas-Rapoport conjecture on the existence of canonical integral models of Shimura varieties with parahoric level structure in the case where the Shimura variety is defined by a torus. As an important ingredient, we show, using the Bhatt-Scholze theory of prismatic $F$-crystals, that there is a fully faithful functor from $\mathcal{G}$-valued crystalline representations of Gal$(\bar{K}/K)$ to $\mathcal{G}$-shtukas over Spd$(\mathcal{O}_K)$, where $\mathcal{G}$ is a parahoric group scheme over $\mathbb{Z}_p$ and $\mathcal{O}_K$ is the ring of integers in a $p$-adic field $K$. |
| title | Canonical integral models for Shimura varieties of toral type |
| topic | Number Theory Algebraic Geometry 11G18 |
| url | https://arxiv.org/abs/2207.09513 |