Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917536614842368 |
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| author | Qijun, Yan Chao, Zhang |
| author_facet | Qijun, Yan Chao, Zhang |
| contents | In this paper, we study the behavior of Ekedahl-Oort strata under natural embeddings between the good reductions modulo $p$ of GSpin Shimura varieties and Rapoport-Smithling-Zhang unitary Shimura varieties, a prototypical setting for the construction of special cycles in the Kudla program. In each case, we determine the EO stratum containing the image of a given EO stratum under the embedding. We also compute discrete invariants of these Shimura varieties, including their $p$-ranks and $a$-numbers; in the GSpin case, these are obtained via the Kuga-Satake embedding. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27207 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties Qijun, Yan Chao, Zhang Number Theory Algebraic Geometry 14G35, 11G18 In this paper, we study the behavior of Ekedahl-Oort strata under natural embeddings between the good reductions modulo $p$ of GSpin Shimura varieties and Rapoport-Smithling-Zhang unitary Shimura varieties, a prototypical setting for the construction of special cycles in the Kudla program. In each case, we determine the EO stratum containing the image of a given EO stratum under the embedding. We also compute discrete invariants of these Shimura varieties, including their $p$-ranks and $a$-numbers; in the GSpin case, these are obtained via the Kuga-Satake embedding. |
| title | Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties |
| topic | Number Theory Algebraic Geometry 14G35, 11G18 |
| url | https://arxiv.org/abs/2605.27207 |