The basic locus of ramified unitary Rapoport-Zink space at maximal vertex level

2025/02/10 by He, Qiao, Luo, Yu, Shi, Yousheng · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.06218

Abstract

We construct the Bruhat-Tits stratification of the ramified unitary Rapoport-Zink space, 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 isomorphism between Bruhat-Tits strata and Deligne-Lusztig varieties, revealing new phenomena beyond the previously studied Coxeter-type cases.

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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