On special subvarieties of Kuga varieties II

TL;DR

This paper proves the equidistribution of certain special subvarieties in Kuga varieties, advancing the understanding of the André-Oort conjecture for mixed Shimura varieties by leveraging results on small points and previous equidistribution theorems.

Contribution

It establishes the equidistribution of $ ext{C}$-special subvarieties in specific Kuga varieties, contributing a significant case towards the André-Oort conjecture for mixed Shimura varieties.

Findings

Proves equidistribution of $ ext{C}$-special subvarieties in certain Kuga varieties.

Reduces equidistribution to known theorems on small points and previous equidistribution results.

Advances the understanding of the André-Oort conjecture for mixed Shimura varieties.

Abstract

In this paper we prove the equidistribution of $\Cbf$-special subvarieties in certain Kuga varieties, which implies a special case of the general Andr\'e-Oort conjecture formulated for mixed Shimura varieties proposed by R.Pink. The main idea is to reduce the equidistribution to a theorem of Szpiro-Ullmo-Zhang on small points of abelian varieties and a theorem on the equiditribution of $C$-special subvarieties of Kuga varieties of rigid type treated by the author in a previous paper.