14 problems

Minimal-valuation local semistable reduction conjecture. $\mathcal{E}$ admits local semistable reduction at any minimal valuation $v$ on $k(X)$ centered on $\overline{X}$.

Let $X$ be a smooth irreducible $k$-variety, let $\overline{X}$ be a partial compactification of $X$, and let $\mathcal{E}$ be an $F$-isocrystal on $X$ overconvergent along…

Let $k$ be a field of characteristic $p>0$, let $K$ be the fraction field of a complete mixed characteristic discrete valuation ring with residue field $k$, and let $X$ be a smooth…

Let $X$ be a regular $p$-adic formal scheme, and let $Y_\eta\to X_\eta$ be a proper smooth rigid space with analytically good reduction over $X_\eta$. For each $i\in\mathbb{N}$, an…

Let $X$ be a smooth curve over $k$. An $F$-isocrystal on $X$ may have a monodromy group in the overconvergent setting and, when it is dagger-extendable, a corresponding dagger mono…

Let $X_i$ be spaces equipped with commuting partial Frobenius actions, and let $X/\Phi$ be the associated partial Frobenius quotient. Let $F$-isocrystals denote $p$-adic isocrystal…

Let $K[[x]]_0$ denote the ring of analytic functions on the unit open disc with log-growth at most $0$, and for $\lambda\geq0$ let $K[[x]]_\lambda$ be the corresponding space of fu…

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

Let $U$ be a smooth curve over $k$ with compactification $C$. Let $M$ be an irreducible overconvergent $F$-isocrystal on $U$ whose fiber Newton polygon is constant as $x$ varies in…

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

Finite-determinant conjecture. There exist elements $u\in\mathbb{Z}_{q'}^*$ such that $(\det V,\det\nabla,u\det\Phi)$ corresponds to a finite character of

Let $X\to S\subseteq \mathbb A^1_{\mathbb F_q}\setminus\{0\}$ be a morphism of varieties over $\mathbb F_q$ with a good lift around $t=0$. Let…