André–Oort–Pink conjecture for mixed Shimura varieties

Let $M$ be a mixed Shimura variety, and let $Z\subset M$ be an arbitrary closed subvariety. Let $\Sigma(Z)$ be the set of special subvarieties of $M$ contained in $Z$, and let $\Sigma_{\mathrm{max}}(Z)$ be the subset of maximal special subvarieties in $\Sigma(Z)$ under inclusion.

André–Oort–Pink conjecture. The set $\Sigma_{\mathrm{max}}(Z)$ is finite.

This is the mixed-Shimura-variety form of the André–Oort conjecture and predicts finiteness of the maximal special subvarieties contained in any closed subvariety. The paper proves equidistribution results for certain families of special subvarieties, but the general conjecture remains open.