Sub-Shimura Varieties for type O(2,n)

TL;DR

This paper classifies sub-Shimura varieties associated with orthogonal groups of signature (2,n) over Q, providing a comprehensive understanding of their structure up to component groups.

Contribution

It offers a complete classification of sub-Shimura varieties for orthogonal groups of signature (2,n), advancing the understanding of their geometric and arithmetic properties.

Findings

Classification of sub-Shimura varieties achieved

Results applicable to orthogonal groups over Q

Enhanced understanding of Shimura variety structures

Abstract

We give a classification, up to consideration of component groups, of sub-Shimura varieties of those Shimura Varieties attached to orthogonal groups of signature (2,n) over Q.