7 problems

Let convergent and overconvergent $F$-isocrystals be coefficient objects in the relevant $p$-adic cohomological categories, with morphisms considered in the convergent category. Ts…

Let $X$ be a connected smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. Let $\mathrm{R}p\mathrm{MT}^w$ d…

Let $X$ be a connected smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. Relative p-adic monodromy conjec…

Let $X$ be a smooth rigid-analytic space over a $p$-adic field $K$, and let $\mathbb{L}$ be a de Rham $\mathbb{Q}_p$-local system on $X$. A point $x\in X$ has rank $1$ if it is a r…

Let $(X,x)$, $X_0$, and $f$ be as in the source, let $u\in\operatorname{fpl}(\Q)$, and let $G(\L_{\mathbf{I},u,X_0},x)$ and $\operatorname{Lg}(f)_{\Q_u}$ be the groups defined ther…

Let $p$ be an odd prime, let $X_0$ be a smooth geometrically connected variety or a finitely generated field over F_{\infty}_p, and let f_0:X_0\to\A_{g,F_{\infty}_p} be a morph…

Maximal monodromy conjecture. The monodromy of a versal family of ordinary Barsotti–Tate groups in characteristic $p>0$ is maximal.