On Special Subvarieties of Kuga Varieties

TL;DR

This paper proves the equidistribution of special subvarieties in Kuga varieties, advancing the understanding of the Andre-Oort conjecture for mixed Shimura varieties using ergodic theory techniques.

Contribution

It establishes the equidistribution of certain special subvarieties in Kuga varieties, a key step towards the mixed Shimura case of the Andre-Oort conjecture.

Findings

Proves equidistribution of special subvarieties in Kuga varieties

Extends techniques from pure to mixed Shimura varieties

Supports the broader Andre-Oort conjecture framework

Abstract

In this paper we prove the equidistribution of certain families of special subvarieties in Kuga varieties, which is a special case of the general Andre-Oort conjecture formulated for mixed Shimura varieties proposed by R.Pink. Our approach is parallel to the pure case treated in the works of L.Clozel, E.Ullmo, and A.Yafaev using tools from ergodic theory.