5 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…

Defect condition. Every mixed Shimura variety, and every weakly special subvariety, has the defect condition. The supplied span does not give the formal definition of the defect co…

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…