The Shafarevich finiteness conjecture for motives

Fix nonnegative integers $h^{r,w-r}$ as above and a set $S$ of prime numbers. Let $F$ be the underlying number field, let $w$ be the weight, and let $M$ be a pure $\mathbb Z$-motive over $F$ with de Rham realization $M_{\operatorname{dR}}$. Shafarevich's conjecture. There are finitely many isomorphism classes of pure $\mathbb Z$-motives of weight $w$ such that

$$\dim\operatorname{gr}^r(M_{\operatorname{dR}})=h^{r,w-r},$$

and which have pure good reduction outside $S$ and semistable reduction inside $S$. The source presents this as a finiteness analogue of the Shafarevich conjecture and says that the version without the purity condition should also hold; no resolution is supplied.