On certain integral Frobenius period maps for Shimura varieties and their reductions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910968297029632 |
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| author | Yan, Qijun |
| author_facet | Yan, Qijun |
| contents | We formulate an integral Frobenius period map for the framed crystalline prismatization of the $p$-integral model $\mathcal{S}$ of a Shimura variety with good reduction. By analyzing reductions of this map, we derive a period map from the mod $p$ fiber $S$ of $\mathcal{S}$ to the moduli stack of 1-1 truncated local $G$-shtukas in the prismatic topology, which refines the zip period map of $S$ within this topology. Furthermore, we show that the pair $(\mathcal{S}, S)$ is associated with a double $G$-zip. Additionally, we introduce a framework of base reduction diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On certain integral Frobenius period maps for Shimura varieties and their reductions Yan, Qijun Algebraic Geometry 14G35, 14G45, 11G18 We formulate an integral Frobenius period map for the framed crystalline prismatization of the $p$-integral model $\mathcal{S}$ of a Shimura variety with good reduction. By analyzing reductions of this map, we derive a period map from the mod $p$ fiber $S$ of $\mathcal{S}$ to the moduli stack of 1-1 truncated local $G$-shtukas in the prismatic topology, which refines the zip period map of $S$ within this topology. Furthermore, we show that the pair $(\mathcal{S}, S)$ is associated with a double $G$-zip. Additionally, we introduce a framework of base reduction diagrams. |
| title | On certain integral Frobenius period maps for Shimura varieties and their reductions |
| topic | Algebraic Geometry 14G35, 14G45, 11G18 |
| url | https://arxiv.org/abs/2501.06601 |