4 problems

Specialness conjecture. Both $H_i$ are weakly special subvarieties with respect to the $\mathbb Z$-PVHS associated with the universal family.

Finiteness conjecture. There exists a finite set $\Sigma_{\mathrm{p}}\cup\Sigma_M$, where $\Sigma_{\mathrm{p}}$ consists of weakly special product subvarieties and $\Sigma_M$ consi…

Specialness conjecture. For any maximal non-rigid family $H_1\times H_2\to M$, both $H_i$ are weakly special subvarieties with respect to the $\mathbb Z$-PVHS of the universal fami…

Let $S$ be a Shimura variety and let ${\mathcal X}$ be a complex realisation of a connected component $X^+$. Let … be the uniformisation map, and let $V$ be an algebraic subvariety…