The prismatic realization functor for Shimura varieties of abelian type
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916704195444736 |
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| author | Imai, Naoki Kato, Hiroki Youcis, Alex |
| author_facet | Imai, Naoki Kato, Hiroki Youcis, Alex |
| contents | For the integral canonical model $\mathscr{S}_{\mathsf{K}^p}$ of a Shimura variety $\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$ of abelian type at hyperspecial level $K_0=\mathcal{G}(\mathbb{Z}_p)$, we construct a prismatic $F$-gauge model for the `universal' $\mathcal{G}(\mathbb{Z}_p)$-local system on $\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$. We use this to obtain several new results about the $p$-adic geometry of Shimura varieties, notably an abelian-type analogue of the Serre--Tate deformation theorem (realizing an expectation of Drinfeld in the abelian-type case) and a prismatic characterization of these models at individual level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08472 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The prismatic realization functor for Shimura varieties of abelian type Imai, Naoki Kato, Hiroki Youcis, Alex Number Theory Algebraic Geometry For the integral canonical model $\mathscr{S}_{\mathsf{K}^p}$ of a Shimura variety $\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$ of abelian type at hyperspecial level $K_0=\mathcal{G}(\mathbb{Z}_p)$, we construct a prismatic $F$-gauge model for the `universal' $\mathcal{G}(\mathbb{Z}_p)$-local system on $\mathrm{Sh}_{\mathsf{K}_0\mathsf{K}^p}(\mathbf{G},\mathbf{X})$. We use this to obtain several new results about the $p$-adic geometry of Shimura varieties, notably an abelian-type analogue of the Serre--Tate deformation theorem (realizing an expectation of Drinfeld in the abelian-type case) and a prismatic characterization of these models at individual level. |
| title | The prismatic realization functor for Shimura varieties of abelian type |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2310.08472 |