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

TL;DR

This paper investigates the structure of the moduli space of abelian threefolds with Iwahori level structure in positive characteristic, analyzing stratifications and fiber structures to deepen understanding of these geometric objects.

Contribution

It explicitly determines the fibers of the canonical projection and explores the relationships between various stratifications on the moduli space.

Findings

Explicit fiber descriptions of the projection map.

Relationships between Ekedahl-Oort, Kottwitz-Rapoport, and Newton stratifications.

Insights into the geometry of abelian threefold moduli spaces.

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.