Suppose $M$ is an object of the (conjectured) abelian category of mixed motives over $\mathbb{Q}$, $\textbf{MM}_{\mathbb{Q}}$, Scholl defines that $M$ is defined over $\mathbb{Z}$ if the following condition is satisfied.

Let $M_{\ell}$ be the $\ell$-adic realisation of $M$, which has a weight filtration $W_*$. For every $ p \neq \ell$, when we consider $M_{\ell}$ as a representation of the inertia group $I_p$, the weight filtration $W_*$ splits.

Suppose $X$ is a hypersurface of the projective space $\mathbb{P}^n_{\mathbb{Z}}$, and let $h^i(X)$ be the mixed motive associated to its $i$-th cohomology, is $h^i(X)$ (expected to be) a mixed motive defined over $\mathbb{Z}$?

If we further assume the singularity of $Y$ consists of finitely many $\mathbb{Z}$-valued points, then is $h^i(X)$ (expected to be) a mixed motive defined over $\mathbb{Z}$?

Here let's assume the existence of the category of mixed motives and its expected properties!