The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915528784740352 |
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| author | Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra |
| author_facet | Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra |
| contents | This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which $p$ is inert. We completely describe the interaction of two stratifications of these Shimura varieties: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra Number Theory Algebraic Geometry 11G18, 14G35, 11G10 This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which $p$ is inert. We completely describe the interaction of two stratifications of these Shimura varieties: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect. |
| title | The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety |
| topic | Number Theory Algebraic Geometry 11G18, 14G35, 11G10 |
| url | https://arxiv.org/abs/2510.01090 |