The monodromy weight conjecture for ℓ-adic cohomology

Let $K$ be a non-archimedean local field with finite residue field $k$, let $X$ be a smooth projective variety over $K$, and let $M_\cdot$ be the monodromy filtration on $H^n(\overline{X},\mathbb Q_\ell)$, with graded pieces regarded as representations of $G_k$. Monodromy weight conjecture. The $G_k$-representation $Gr^M_iH^n(\overline{X},\mathbb Q_\ell)$ is pure of weight $n+i$. This was proved by Deligne in the equi-characteristic case under the geometric hypotheses stated in the source, so the conjecture is solved in that case; the general mixed-characteristic statement is not resolved here.