The hybrid conjecture for Shimura varieties

Let $(M,X_M)$ and $(G,X)$ be Shimura data, let $x\bin X_M$ be Hodge generic, and let $\bSigma$ be the image in $Sh_K(G,X)$ of the hybrid orbit of $(M,X_M,x)$. Let $V\bsubseteq Sh_K(G,X)$ be an irreducible subvariety. Hybrid conjecture. If

$$V\cap \Sigma$$

is Zariski dense in $V$, then $V$ is weakly special. This is presented as a common generalisation of the André–Oort and generalised André–Pink–Zannier conjectures; the paper proves it for Shimura varieties of abelian type.