11 problems

Let $\mathcal{Y}$ be a gerbe with dual $\widehat{\mathcal{Y}}$ and associated $\mathbb{C}^*$-gerbe $c$. Let $D\subset \mathcal{B}$ be a smooth irreducible divisor, and define its i…

The obstruction conjecture. The obstruction to the gerbe $R$ over $D$ being trivial equals the obstruction to the normal bundle $N_{D/X}$ having an $n$-th root as a line bundle on…

Let $\mathcal{X}$ and $\mathcal{Y}$ be smooth Deligne--Mumford stacks with Gorenstein moduli spaces $X$ and $Y$. Suppose there are birational maps … such that $f^*K_X=g^*K_Y$. The…

Real stack Smith–Thom conjecture. The dimension of the mod-$2$ cohomology of the real locus should satisfy

Let $G$ be a finite group, let $Q$ act on the finite set of isomorphism classes of irreducible $G$-representations, and let $\mathcal{Y}$ be a gerbe with dual…

KD hypothesis. If $(X,B)\sim_K(Y,C)$, then there is an equivalence

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 $\mathcal{X}$ be a Deligne–Mumford stack of finite type over $D$, and let $\mathcal{J}_{\infty}\mathcal{X}$ be its moduli space of twisted arcs. For $n\in\mathbb{Z}_{\ge0}$, a…

Let $\mathcal{X}$ be a Deligne–Mumford stack of finite type over $D$. A stacky formal disk is a connected normal Deligne–Mumford stack birational and finite over $D$, and a twisted…

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…

BorisovHua conjecture. Every smooth nef-Fano toric DM stack possesses a full strong exceptional collection of line bundles.