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Regular models of ramified unitary Shimura varieties at maximal parahoric level

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arxiv 2410.04500 v2 pith:YBTPVKO6 submitted 2024-10-06 math.AG math.NT

Qiao He , Yu Luo , Yousheng Shi This is my paper
classification math.AGmath.NT
keywords modelsplittingcaseflatlevelmaximalmodelsparahoric
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abstract

We use the idea of splitting models to define and study a semi-stable model for unitary Shimura varieties of signature $(n-1,1)$ with maximal parahoric level structure at ramified primes. In this case, the ``naive'' splitting model defined by Pappas and Rapoport fails to be flat in a crucial way. We prove that the genuine splitting model in this case is flat with semi-stable reduction.

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

    math.AG 2025-02 unverdicted novelty 6.0 of 10

    Constructs Bruhat-Tits stratification for ramified unitary Rapoport-Zink space of signature (n-1,1) at vertex lattice level, proves normality, Cohen-Macaulayness and dimension formulas, and gives scheme-theoretic isom...

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