Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912621313130496 |
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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 $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: 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. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ 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 $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: 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. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$. |
| title | Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety |
| topic | Number Theory Algebraic Geometry 11G18, 14G35, 11G10 |
| url | https://arxiv.org/abs/2405.04464 |