Hybrid André-Oort–André-Pink-Zannier conjecture

Let $\Gamma\backslash X^+$ be an arithmetic variety, let $V$ be an irreducible algebraic subvariety, let $(M,X_M)$ be a Shimura datum, and let $x\in X_M$ be Hodge generic. Write $\Sigma_{\Gamma\backslash X^+}(M,X_M,x)$ for the associated set defined in the paper. Hybrid André-Oort–André-Pink-Zannier conjecture. The Zariski closure of $\Sigma_{\Gamma\backslash X^+}(M,X_M,x)\cap V$ is a finite union of weakly special subvarieties of $\Gamma\backslash X^+$. The source explains that this specialises to André–Oort for special $x$ and implies the generalised André–Pink–Zannier conjecture; no general proof is given.