On the Piatetski-Shapiro construction for integral models of Shimura varieties
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929732990271488 |
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| author | van Hoften, Pol Sempliner, Jack |
| author_facet | van Hoften, Pol Sempliner, Jack |
| contents | We study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the Gamma-fixed points of the Shimura varieties for (H,Y) recover the Shimura varieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type with parahoric level, we show that the same is true for the p-adic integral models constructed by Pappas--Rapoport. We also study the Gamma-fixed points of the Igusa stacks of Zhang for (H,Y) and prove optimal results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Piatetski-Shapiro construction for integral models of Shimura varieties van Hoften, Pol Sempliner, Jack Number Theory Algebraic Geometry 11G18, 14G35 We study the Piatetski-Shapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the Gamma-fixed points of the Shimura varieties for (H,Y) recover the Shimura varieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type with parahoric level, we show that the same is true for the p-adic integral models constructed by Pappas--Rapoport. We also study the Gamma-fixed points of the Igusa stacks of Zhang for (H,Y) and prove optimal results. |
| title | On the Piatetski-Shapiro construction for integral models of Shimura varieties |
| topic | Number Theory Algebraic Geometry 11G18, 14G35 |
| url | https://arxiv.org/abs/2403.10653 |