Bounded eqidistribution of special subvarieties in mixed Shimura varieties

TL;DR

This paper proves the equidistribution of bounded sequences of special subvarieties in mixed Shimura varieties, extending pure case results and exploring their relation to Galois orbits, contributing to the understanding of the Andre-Oort conjecture.

Contribution

It establishes the equidistribution of bounded sequences of special subvarieties in mixed Shimura varieties, generalizing previous pure case results.

Findings

Bounded sequences of special subvarieties are equidistributed in mixed Shimura varieties.

The paper relates bounded sequences to bounded Galois orbits of special subvarieties.

Provides insights into the structure of special subvarieties in the context of the Andre-Oort conjecture.

Abstract

In this paper we prove the equidistribution of bounded sequences of special subvarieties in a general mixed Shimura varieties, a notion adapted from the pure case treated by Clozel, Ullmo, and Yafaev in the study of the Andre-Oort conjecture. We also discuss the relation of bounded sequences with bounded Galois orbits of special subvarieties.