Weights conjecture for intersection cohomology of rigid-analytic varieties

Let $K$ be a $p$-adic local field with residue field of cardinality $q$, let $X$ be a quasi-compact and quasi-separated rigid-analytic $K$-variety of dimension $d$, and let $\ell\neq p$ be a prime number. Let $G_\eta$ and $G_s$ denote the relevant generic- and special-fiber Galois groups, and let $\operatorname{IH}^i_c$ and $\operatorname{IH}^i$ denote compactly supported and ordinary intersection cohomology. Weights conjecture. For any $g\in G_\eta$ projecting to geometric Frobenius in $G_s$ and any integer $i\geq0$, the eigenvalues of $g$ on

$$\operatorname{IH}^i_c(X_{\bar\eta};\Q_\ell)$$

are $q$-Weil numbers of weights at most $2i+d$, and the eigenvalues on

$$\operatorname{IH}^i(X_{\bar\eta};\Q_\ell)$$

are $q$-Weil numbers of weights at least $0$. In particular, when $X$ is smooth and proper, the eigenvalues on $\rm{H}^i(X_{\overline{\bar\eta}},\Q_\ell)$ have weights between $0$ and $2i$. This conjecture extends known weight bounds from algebraic varieties to general quasi-compact quasi-separated rigid-analytic varieties; the smooth proper algebraic case is noted in the source as known via alterations and semistable results, while the analytic assertion remains open.