Integral models of certain PEL-Shimura varieties with Γ₁(p)-type level structure

2013/09/13 by Richard Shadrach, Shadrach, Richard
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1309.3485

openalex publication_date 2013/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study p-adic integral models of certain PEL Shimura varieties with level subgroup at p related to the Γ₁(p)-level subgroup in the case of modular curves. We will consider two cases: the case of Shimura varieties associated with unitary groups that split over an unramified extension of ℚ_p and the case of Siegel modular varieties. We construct local models, i.e. simpler schemes which are étale locally isomorphic to the integral models. Our integral models are defined by a moduli scheme using the notion of an Oort-Tate generator of a group scheme. We use these local models to find a resolution of the integral model in the case of the Siegel modular variety of genus 2. The resolution is regular with special fiber a nonreduced divisor with normal crossings.

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