On the flatness of models of certain Shimura varieties of PEL-type

1999/12/08 by Ulrich Goertz, Goertz, U. · 7 citations
Mathematics · #14G35 (Primary) 11G18 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/9912064

openalex publication_date 1999/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a PEL-Shimura variety associated to a unitary group that splits over an unramified extension of Q_p. Rapoport and Zink have defined a model of the Shimura variety over the ring of integers of the completion of the reflex field at a place lying over p, with parahoric level structures at p. We show that this model is flat, as conjectured by Rapoport and Zink, and that its special fibre is reduced.

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• Topological flatness of orthogonal spin local models
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• Trace of Frobenius on nearby cycles for a Γ₁(p)-local model
• On the geometry of integral models of Shimura varieties with Γ₁(p)-level structure
• Dual Shellability of Admissible Set and Cohen-Macaulayness of Local Models
• Global positroid varieties

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