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arXiv · 2605.27207

Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties

Yan Qijun·Zhang Chao
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Abstract

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.

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Yan Qijun, Zhang Chao. 2026-05-26. Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties. https://arxiv.org/abs/2605.27207

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