The p-rank stratification on the Siegel moduli space with Iwahori level structure

TL;DR

This paper investigates the structure of p-rank stratification on Siegel moduli spaces with Iwahori level structure in positive characteristic, focusing on dimensions, closures, and relations to other stratifications.

Contribution

It provides explicit calculations of the dimensions and closures of p-rank strata and explores their relationship with Kottwitz-Rapoport stratification.

Findings

Dimension formulas for p-rank strata

Descriptions of closure relations among strata

Connections between p-rank and Kottwitz-Rapoport stratifications

Abstract

Our concern in this paper is to describe the p-rank statification on the Siegel moduli space with Iwahori level structure over fields of positive characteristic. We calculate the dimension of the strata and describe the closure of a given stratum in terms of p-rank strata. We also examine the relationship between the p-rank stratification and the Kottwitz-Rapoport stratification.