Intersections of the Ekedahl-Oort and Newton Strata of $\mathcal{A}_{5}$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910098457100288 |
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| author | Groen, Steven R. Lupoian, Elvira Parker, Mychelle |
| author_facet | Groen, Steven R. Lupoian, Elvira Parker, Mychelle |
| contents | The moduli space $\mathcal{A}_g$ of principally polarised abelian varieties of dimension $g$, defined over an algebraically closed field of characteristic $p >0$, is studied through various stratifications. The two most prominent ones are the Newton stratification, based on the isogeny class of the $p$-divisible group of an abelian variety, and the Ekedahl-Oort stratification, defined by the isomorphism class of its $p$-torsion group scheme. In general, it is not known how the strata of these two intersect. In this paper we completely determine which of these intersections are non-empty in dimension five. As a consequence, we give an explicit description of the induced Ekedahl-Oort stratification on the supersingular locus $\mathcal{S}_{5}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of the Ekedahl-Oort and Newton Strata of $\mathcal{A}_{5}$ Groen, Steven R. Lupoian, Elvira Parker, Mychelle Algebraic Geometry Number Theory 14L05, 14G17, 11G10 The moduli space $\mathcal{A}_g$ of principally polarised abelian varieties of dimension $g$, defined over an algebraically closed field of characteristic $p >0$, is studied through various stratifications. The two most prominent ones are the Newton stratification, based on the isogeny class of the $p$-divisible group of an abelian variety, and the Ekedahl-Oort stratification, defined by the isomorphism class of its $p$-torsion group scheme. In general, it is not known how the strata of these two intersect. In this paper we completely determine which of these intersections are non-empty in dimension five. As a consequence, we give an explicit description of the induced Ekedahl-Oort stratification on the supersingular locus $\mathcal{S}_{5}$. |
| title | Intersections of the Ekedahl-Oort and Newton Strata of $\mathcal{A}_{5}$ |
| topic | Algebraic Geometry Number Theory 14L05, 14G17, 11G10 |
| url | https://arxiv.org/abs/2509.19878 |