Unitary Shimura-subvariety disjointness conjecture for the Torelli locus

Let $M\subset\mathcal{A}_g$ be a Shimura subvariety of the unitary type specified earlier in the source. Unitary disjointness conjecture. The intersection

$$\mathcal{T}_g^\circ\cap M$$

is empty. The conjecture is motivated by the theorem proved in the paper and is restricted to the indicated unitary class because the analogous assertion fails for arbitrary weakly special or Shimura subvarieties: Hilbert modular varieties can contain Teichmüller curves lying in the open Torelli locus. The proposed assertion is not resolved in the supplied text.