Heights on 'Hybrid orbits' in Shimura varieties

TL;DR

This paper proves the hybrid conjecture, unifying the Andrée-Oort and Andrée-Pink-Zannier conjectures, for Shimura varieties of abelian type, advancing understanding of special points and subvarieties in these complex algebraic structures.

Contribution

It establishes the hybrid conjecture for Shimura varieties of abelian type, generalizing key conjectures in arithmetic geometry.

Findings

Proves the hybrid conjecture in the abelian type case

Unifies the Andrée-Oort and Andrée-Pink-Zannier conjectures

Enhances understanding of special subvarieties in Shimura varieties

Abstract

We prove the 'hybrid conjecture' which is a common generalisation of the Andre\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture, in the case of Shimura varieties of abelian type.