Deformation theory for prismatic $G$-displays
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917906990759936 |
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| author | Ito, Kazuhiro |
| author_facet | Ito, Kazuhiro |
| contents | For a smooth affine group scheme $G$ over the ring of $p$-adic integers and a cocharacter $μ$ of $G$, we develop the deformation theory for $G$-$μ$-displays over the prismatic site of Bhatt-Scholze, and discuss how our deformation theory can be interpreted in terms of prismatic $F$-gauges introduced by Drinfeld and Bhatt-Lurie. As an application, we prove the local representability and the formal smoothness of integral local Shimura varieties with hyperspecial level structure. We also revisit and extend some classification results of $p$-divisible groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05361 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation theory for prismatic $G$-displays Ito, Kazuhiro Number Theory Algebraic Geometry Primary 14F30, Secondary 14G45, 11G18, 14L05 For a smooth affine group scheme $G$ over the ring of $p$-adic integers and a cocharacter $μ$ of $G$, we develop the deformation theory for $G$-$μ$-displays over the prismatic site of Bhatt-Scholze, and discuss how our deformation theory can be interpreted in terms of prismatic $F$-gauges introduced by Drinfeld and Bhatt-Lurie. As an application, we prove the local representability and the formal smoothness of integral local Shimura varieties with hyperspecial level structure. We also revisit and extend some classification results of $p$-divisible groups. |
| title | Deformation theory for prismatic $G$-displays |
| topic | Number Theory Algebraic Geometry Primary 14F30, Secondary 14G45, 11G18, 14L05 |
| url | https://arxiv.org/abs/2306.05361 |