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arXiv · 2502.06218

The basic locus of ramified unitary Shimura varieties of signature $(n-1,1)$ at maximal vertex level

Qiao He·Yu Luo·Yousheng Shi
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Abstract

We construct the Bruhat--Tits stratification of the reduced locus of the ramified unitary Rapoport--Zink space of signature $(n-1,1)$, with the level being the stabilizer of a vertex lattice. We develop the local model theory for Bruhat--Tits strata, proving their normality and Cohen--Macaulayness, and provide precise dimension formulas. Additionally, we establish an explicit scheme-theoretical isomorphism between Bruhat--Tits strata and Deligne--Lusztig varieties.

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Qiao He, Yu Luo, Yousheng Shi. 2025-02-10. The basic locus of ramified unitary Shimura varieties of signature $(n-1,1)$ at maximal vertex level. https://arxiv.org/abs/2502.06218

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