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

2025/02/10 by Qiao He, Yu Luo, He, Qiao +3 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.06218

openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level
• The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level

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