6 problems

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 $S$ 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 $D=\operatorname{Spec}A$, 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…