13 problems

Vistoli's conjecture. If

Subgroup-fixed-locus compatibility conjecture. These inclusions commute with Iritani's partial isomorphisms and with the action of $\mathsf{MT}$. This generalizes the preceding com…

Let $X$ be a smooth projective variety with a $G$-action, let $Z\subset X$ be a $G$-invariant submanifold of codimension $c\geq 2$, and set $\widetilde X=\operatorname{Bl}_Z(X)$ an…

Let $X$ be a smooth projective variety with an action of a group $G$, and let $Z\subset X$ be a $G$-invariant submanifold of codimension $c\geq 2$. Write … with $c-1$ copies of $Z$…

Let $X$, $G$, and $\mathcal{E}$ be as in the surrounding construction, with $G$ finite, and let $\pi:[\mathbb{A}(\mathcal{E})/G]\rightarrow[X/G]$ be the induced projection. Suppose…

Let $T_2$ be the torus acting on $V_1$ with character $t_1$ and on $V^*$ with character $t_2$, where $t_1,t_2\in\mathfrak{t}_2^*$ are the projections onto the respective factors. L…

BPS complex conjectures. The following assertions should hold:

Let $G$ be a reductive group scheme, let $X$ be a space with the quotient simplicial object $[X/G]_{\bullet}$, and let $Cpx$ denote the functor sending a space to the dg-category o…

Let $X$ be an algebraic stack locally of finite type over an algebraically closed field $k$ with separated and quasi-compact diagonal, and suppose that $X$ has affine stabilizer gr…

Let $\phi:\mathcal{X}=[M/G]\to X=M/G$ be the proper birational morphism associated with a $G$-variety $M$. Let $\gamma:\mathcal{E}\to\mathcal{X}$ be a twisted arc whose generic poi…

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 $\mathcal{X}$ be a finite type Artin stack over $\operatorname{Spec} k$, and let $xin\robots.txtmathcal{X}(k)$ have linearly reductive stabilizer $G_x$. An algebraic space $X$…

Alper's étale-local quotient conjecture. There exists an étale neighborhood $S'\to S$ with $s'\mapsto s$ and an étale, representable morphism