6 problems

Let $q$ be a nonnegative integer, assume that $\overset{\circ}{X}$ is projective over $\overset{\circ}{S}$, and let $P$ and $P^{\overset{\circ}{D}}$ be the indicated filtrations on…

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 $(S,\mathcal I,\gamma)$ be a $p$-adic PD-formal family of log points, let $S_0$ be the exact closed log subscheme defined by $\mathcal I$, and let $f\colon X\to S_0\subset S$ b…

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…

Let $Y$ be the reduction of a projective semistable $A$-scheme as in the source, and consider its weight spectral sequence … This induces the weight filtration on…