4 problems

Let $A$ be an abelian variety over a finite extension $F$ of $\mathbb Q$, let $p>2\dim(A)+1$ be prime, let $F_\infty=F(A_{p^\infty})$, and put…

Let $\bar{A}$ be one of the coefficient objects considered in the source, with coefficient ring $\bar{R}$, and let $F_\infty/F$ be a $p$-adic Lie extension such that…

Let $F$ be a number field, let $\widetilde{F}$ be the compositum of all $\mathbb{Z}_{p}$-extensions of $F$, and let $K(\widetilde{F})$ be the maximal unramified abelian pro-$p$ ext…

Let $M$ be an irreducible overconvergent $F$-isocrystal on $\operatorname{Spec}(F)$ with nonnegative slopes. Let $M^{u-r}$ be its unit-root subcrystal, and let $\eta$ be its first…