4 problems

Let $K$ be the local field, let $X$ be a proper smooth variety over $K$, and let $H^j(X^{\mathrm{ca}},\overline{\mathbb{Q}}_l)$ carry its monodromy filtration $M_\bullet$ and weigh…

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…

Let $K$ be a complete discrete valuation field of characteristic zero with finite residue field $k$ of characteristic $p$, let $W_K$ be its Weil group with valuation map $v$, and l…

Mixedness conjecture. Every $\overline{\mathbb{Q}}_{\ell}$-coefficient object on $X_0$ is $\iota$-mixed.