13 problems

Let $S$ be a strictly henselian trait with geometric generic point $\bar\eta$. Let $p:X\to S$ be regular, flat, proper, and generically smooth. Write $X_s$ and $X_{\bar\eta}$ for t…

Let $X$ be a smooth projective curve over a finite field, let $S\subseteq X$ be a set of marked points, and consider rank-$2$ $\ell$-adic local systems on…

Let $k$ be an algebraically closed field of characteristic $p>0$. Let $\phi: Z \xrightarrow{} X$ be a cyclic $\Gamma$-cover of curves over $k$, and let $\phi_1: Y \xrightarrow{} X$…

Let $p$ be prime, and consider a wild action of $\mathbb{Z}/p\mathbb{Z}$ on a two-dimensional regular local scheme whose quotient has a wild cyclic quotient singularity. An action…

Let $S$ be a strictly henselian trait with algebraically closed residue field, and let $X$, $x$, $\mathcal F$, and $\mathcal F'$ be as in Theorem: $X$ is a strictly local $S$-schem…

Let $K$ be a complete discretely valued field with algebraically closed residue field of characteristic $p$. Let $L/K$ be a $\mathbb{Z}/p$-extension, let $s$ be the jump in its ram…

Let $D=\operatorname{Spec}A$ and let $G$ be a finite group. Let $\operatorname{GCov}D$ denote the moduli space of unpointed $G$-covers of $D$, and let constructible subsets be defi…

Let $D=\operatorname{Spec}A$, let $G$ be a finite group, and let $V$ be a $G$-representation over $D$. Put $\mathcal{X}=[V/G]$, and identify its twisted-arc space with the equivari…

Let $D=\operatorname{Spec}A$ and let $\mathcal{X}$ be a Deligne–Mumford stack of finite type and pure dimension over $D$, with twisted-arc space $\mathcal{J}_{\infty}\mathcal{X}$.…

Let $D=\operatorname{Spec}A$ be as above, let $M$ be a $D$-variety endowed with an action of a finite group $G$, and let a G-arc be a $G$-equivariant $D$-morphism $E\to M$ from a…

Let $A$ be a complete discrete valuation ring with algebraically closed residue field, let $D=\operatorname{Spec}A$, and let $G$ be a finite group. A $G$-cover of $D$ is the finite…

Let $A$ be a complete discrete valuation ring with algebraically closed residue field, let $D=\operatorname{Spec}A$, and let $\mathcal{X}$ be a Deligne–Mumford stack of finite type…

Let $X$ be a smooth scheme over $k$, let $D$ be a divisor with simple normal crossings, and let $U=X\setminus D$. Let ${\cal F}$ be a locally constant sheaf of free $\Lambda$-modul…