# The Structure of Integral Parabolic Subgroups of Orthogonal Groups

## TL;DR

This paper analyzes the detailed structure of parabolic subgroups in orthogonal groups over integers and describes their role in the boundary components of toroidal compactifications of orthogonal Shimura varieties.

## Contribution

It provides a comprehensive description of integral parabolic subgroups of orthogonal groups and clarifies their application in the geometry of Shimura varieties.

## Key findings

- Explicit classification of parabolic subgroups over integers
- Description of canonical boundary components in compactifications
- Enhanced understanding of orthogonal Shimura varieties

## Abstract

We determine the detailed structure of parabolic subgroups of orthogonal groups over $\mathbb{Z}$, and deduce the precise form of canonical boundary components in toroidal compactifications of orthogonal Shimura varieties.