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

2025/10/16 by Zachos, Ioannis, Zhao, Zhihao · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.14497

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.

Citations

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Cited by

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

Related

• The basic locus of ramified unitary Shimura varieties of signature (n-1,1) at maximal vertex level
• The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level
• The Bruhat-Tits stratification for basic unramified GU(1,n-1) Rapoport-Zink spaces at arbitrary parahoric level
• On the Bruhat-Tits stratification for GU(2,2) type Rapoport-Zink space: unramified case
• On the cohomology of the ramified PEL unitary Rapoport-Zink space of signature (1,n-1)