  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. We also prove another result, a p-adic
Kempf-Ness theorem, on the relation between good reduction of homogeneous
spaces over p-adic integers with Mumford stability property in p-adic geometric
invariant theory.
