On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure

2009/11/30 by Philipp Hartwig, Hartwig, Philipp · 1 citation
Mathematics · #14G35 #14K10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14G35 #msc:14K10

paper · pdf · doi:10.48550/arxiv.0911.5661

arxiv created 2009/11/30 · openalex publication_date 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study the moduli space of abelian threefolds with Iwahori level structure in positive characteristic. We explicitly determine the fibers of the canonical projection to the moduli space of principally polarized abelian varieties and draw conclusions about the relationship between the Ekedahl-Oort, the Kottwitz-Rapoport and the Newton stratification on these spaces.

Citations

• Introduction to Shimura varieties with bad reduction of parahoric type
• The supersingular locus in Siegel modular varieties with Iwahori level structure

Cited by

• The weight reduction of mod p Siegel modular forms for GSp₄

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• The supersingular locus in Siegel modular varieties with Iwahori level structure
• Alcoves et p-rang des variétés abéliennes
• Ekedahl-Oort strata and Kottwitz-Rapoport strata
• The Kodaira dimension of Siegel modular varieties of genus 3 or higher
• Geometry of the Siegel modular threefold with paramodular level structure