The EKOR-stratification on the Siegel modular variety with parahoric level structure

TL;DR

This paper explores the arithmetic geometry of Siegel modular varieties with parahoric level structure, focusing on the EKOR-stratification and its realization via a smooth morphism into an algebraic stack.

Contribution

It introduces a novel realization of the EKOR-stratification as fibers of a smooth morphism into an algebraic stack parametrizing polarized chains of truncated displays.

Findings

EKOR-stratification is realized as fibers of a smooth morphism.

The study advances understanding of the reduction modulo p of Siegel modular varieties.

Provides a new geometric framework for analyzing stratifications in arithmetic geometry.

Abstract

We study the arithmetic geometry of the reduction modulo $p$ of the Siegel modular variety with parahoric level structure. We realize the EKOR-stratification on this variety as the fibers of a smooth morphism into an algebraic stack parametrizing homogeneously polarized chains of certain truncated displays.