Generalised Andr\'e-Pink-Zannier Conjecture for Shimura varieties of abelian type

Abstract

In this paper we prove the generalised Andr\'e-Pink-Zannier conjecture (an important case of the Zilber-Pink conjecture) for all Shimura varieties of abelian type. Questions of this type were first asked by Y. Andr\'e in 1989. We actually prove a general statement for all Shimura varieties, subject to certain assumptions that are satisfied for Shimura varieties of abelian type and are expected to hold in general