2 problems

Let $X$ be regular, let $W_0$ be the sum of generalized $\phi$-eigenspaces whose eigenvalues are roots of unity, and let $\operatorname{sp}$ be the étale specialization map. Weight…

Let $X$ be regular, and let $W_{i-1}$ denote the indicated weight filtration on the $p$-adic étale cohomology groups of the special and geometric generic fibres. Let…