Weight-monodromy conjecture for smooth proper varieties over local fields

Let $X$ be a proper, smooth, separated scheme of finite type over a non-Archimedean local field $K$, let $l$ be a prime different from the residue characteristic, and let $M_\bullet$ be the monodromy filtration on $\operatorname{H}^i_{\text{\scriptsize ét}}(X_{\overline{K}},\operatorname{\mathbf{Q}}_l)$. Writing $q$ for the cardinality of the residue field and $\mathrm{Fr}_q$ for geometric Frobenius, the graded piece is $\operatorname{Gr}_j^M \operatorname{H}^i_{\text{\scriptsize ét}}(X_{\overline{K}},\operatorname{\mathbf{Q}}_l)$. Weight-monodromy conjecture. The eigenvalues of $\mathrm{Fr}_q$ on $\operatorname{Gr}_j^M \operatorname{H}^i_{\text{\scriptsize ét}}(X_{\overline{K}},\operatorname{\mathbf{Q}}_l)$ are algebraic numbers whose conjugates all have complex absolute values equal to $q^{(i+j)/2}$. This filtration is known to coincide with the weight-monodromy filtration for curves, where the conjecture was proved by Grothendieck; the status supplied for this candidate therefore records the claim as resolved.