André–Pink conjecture for principally polarized abelian varieties

Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties of dimension $g$ over $\mathbb{C}$, let $Z\subset\mathcal{A}_g$ be an irreducible algebraic subvariety, and let $\Sigma$ be a polarized isogeny class in $\mathcal{A}_g$. André–Pink conjecture. If $\Sigma\cap Z$ is Zariski dense in $Z$, then $Z$ is a special subvariety of $\mathcal{A}_g$. This is an André–Pink-type unlikely-intersection statement relating polarized isogeny classes to special subvarieties; the supplied text gives no resolution status.