A classification of Shimura curves in $\mathcal{A}_g$

TL;DR

This paper provides a detailed classification of all one-dimensional Shimura subvarieties within moduli spaces of polarized abelian varieties, based on Shimura data, advancing understanding of their structure.

Contribution

It offers a comprehensive classification framework for 1-dimensional Shimura subvarieties in moduli spaces, linking them explicitly to Shimura data.

Findings

Complete classification of 1-dimensional Shimura subvarieties

Explicit description in terms of Shimura data

Enhanced understanding of the structure of abelian varieties

Abstract

We give a precise classification, in terms of Shimura data, of all 1-dimensional Shimura subvarieties of a moduli space of polarized abelian varieties.