6 problems

Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$, and let $\pi_1(X)$ denote its étale fundamental group. An isocrystal on $X$ i…

Le Stum's conjecture. For any pair $(X,Y)$ over $k$, the functor $\mathrm{sp}_!$ is an equivalence of categories.

Let $C_0$ be a smooth projective curve over the finite field $\mathbb F_q$ of characteristic $p>0$, let $C$ be its base change to $\overline{\mathbb F}_q$, and let $M_K$ and…

Let $X$ be a variety, let $\operatorname{\mathbf{F-Isoc}}^\dagger(X)$ denote the category of overconvergent $F$-isocrystals on $X$, and let $C \subseteq X$ be a curve. Curve restri…

Let $X$ be a variety, let $Y$ be a boundary or compactification datum, and let $C$ denote a curve contained in the indicated variety. Write $\operatorname{\mathbf{F-Isoc}}(X)$ and…

Let $X$ be the fixed variety, and let $\operatorname{\mathbf{F-Isoc}}(X)$ and $\operatorname{\mathbf{F-Isoc}}^\dagger(X)$ denote the categories of convergent and overconvergent $F$…