6 problems

Căldăraru's conjecture. There exists an exact equivalence between the derived categories of twisted coherent sheaves

Let $X$ be a quasi-separated Deligne–Mumford stack with generically trivial stabilizer. Let $\mathcal{M}\in \operatorname{QCoh}(X)$ and let $\alpha\in \mathrm{Br}(X)$. Write…

Let $\pi:{{{{{{{{\mathcal M}}}}}}}}\rightarrow S$ be a deformation of a smooth complex projective variety $M_0$ over a smooth germ $(S,0)$, and write $M_s=\pi^{-1}(s)$. Let…

Let $\mathcal{E}$ be an $\alpha$-twisted locally free sheaf on $\operatorname{Spec}K$ of rank $n$, and let $\mathbb{P}\mathcal{E}$ denote its associated twisted projective space. T…

Jiang's twisted multiple-cover conjecture. If $H^{0,1}(S)=H^{0,2}(S)=0$, there exist rational numbers $\operatorname{VW}^{\operatorname{tw}}_{\alpha_i}({\mathfrak S})$ such that

Let $X$ be a scheme over an ordinary commutative ring $S$, let $p:X\rightarrow\operatorname{Spec} S$ be the structure morphism, and let $\alpha\in\operatorname{Br}(S)$. Write…