4 problems

Let $E$ and $F$ be rigid analytic spaces over a number field $K$, and let $H_{min}(E)$ denote the minimal height arising from the slope filtration of $E$. Bost's conjecture. The mi…

Let $X$, $K$, $\mathcal M^\dagger$, and $\mathcal N^\dagger$ be as in the minimal slope conjecture, with associated convergent $F$-isocrystals $\mathcal M$ and $\mathcal N$. Write…

Let $X$ be a smooth connected scheme separated of finite type over $\operatorname{Spec} k$. Let $\mathcal M^\dagger$ and $\mathcal N^\dagger$ be irreducible overconvergent $F$-isoc…

Let $M$ be an irreducible overconvergent $F$-isocrystal over $\operatorname{Spec}(F)$. Suppose its slope filtration is … with graded pieces of slopes…