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arXiv · 2510.14497

The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level

Ioannis Zachos·Zhihao Zhao
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Abstract

We construct the Bruhat-Tits stratification of the ramified unitary splitting Rapoport-Zink space, with the level being the stabilizer of a vertex lattice. To determine certain local properties of the Bruhat-Tits strata, we develop a theory of the strata splitting models. To study their global structure, we establish an explicit isomorphism between the Bruhat-Tits strata and certain (modified) Deligne-Lusztig varieties.

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Ioannis Zachos, Zhihao Zhao. 2025-10-16. The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level. https://arxiv.org/abs/2510.14497

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