Decidability of singularities in the Ekedahl--Oort stratification
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917351785496576 |
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| author | Koskivirta, Jean-Stefan La Porta, Lorenzo |
| author_facet | Koskivirta, Jean-Stefan La Porta, Lorenzo |
| contents | For an abelian type Shimura variety and an odd prime $p$ of good reduction, we characterize the regularity in codimension one of Zariski closures of Ekedahl--Oort strata in terms of the Frobenius action on the root datum. We give an algorithm that detects codimension one singularities for arbitrary Ekedahl--Oort strata. When the Shimura datum is of split type, we relate the singularities of Ekedahl--Oort strata to a stack of $G$-zips over the complex numbers. We study the existence of generalized Hasse invariants on this stack. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17604 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decidability of singularities in the Ekedahl--Oort stratification Koskivirta, Jean-Stefan La Porta, Lorenzo Number Theory Algebraic Geometry 14G35 (Primary), 14G17, 14D23 (Secondary) For an abelian type Shimura variety and an odd prime $p$ of good reduction, we characterize the regularity in codimension one of Zariski closures of Ekedahl--Oort strata in terms of the Frobenius action on the root datum. We give an algorithm that detects codimension one singularities for arbitrary Ekedahl--Oort strata. When the Shimura datum is of split type, we relate the singularities of Ekedahl--Oort strata to a stack of $G$-zips over the complex numbers. We study the existence of generalized Hasse invariants on this stack. |
| title | Decidability of singularities in the Ekedahl--Oort stratification |
| topic | Number Theory Algebraic Geometry 14G35 (Primary), 14G17, 14D23 (Secondary) |
| url | https://arxiv.org/abs/2603.17604 |