3 problems

Let $\overset{\circ}{S}$ be a $p$-adic formal scheme and let $\overset{\circ}{X}\to\overset{\circ}{S}$ be projective. For a log smooth scheme $Y/S$, let … be the monodromy operator…

Let $X/S_0$ be a proper SNCL scheme with structural morphism $f\colon X\longrightarrow S_0\overset{\subset}{\longrightarrow} S$, and suppose that the relative dimension of…

Log weak Lefschetz conjecture. Assume that $\mathcal O_Y(E)$ is ample. Then the morphism above is a filtered isomorphism with respect to $P$ if $q\leq d-2$ and strictly injective f…