6 problems

Benson's nucleus-support conjecture. The nucleus of $G$ is the same as the support of the singularity category $\mathcal{D}_\text{sg}(C^*(BG))$.

Let $\mathbf T$ be a finite tensor category and let $\underline{\mathbf T}$ be its stable category. Let $C^\bullet_{\underline{\mathbf T}}$ be the categorical center of the cohomol…

Let $\mathbf T$ be a finite tensor category and let $\underline{\mathbf T}$ be its stable category. Write $C^\bullet_{\underline{\mathbf T}}$ for the categorical center of its coho…

A small quantum Borel algebra is associated to a complex simple Lie algebra and a choice of group-like elements; its cohomological support map assigns support data to objects in th…

Let $\CM$ be a category with the action under consideration, and let $\CM^{\on{lisse}}\subset\CM$ denote its lisse subcategory. For an object $m\in\CM$, write $\on{supp}(m)$ for it…

Let $\mathfrak{g}$ be the Lie algebra under consideration, graded by $\mathbb{Z}^n$, and let $V$ be a mixed $\mathfrak{g}$-module: there are weights $\lambda$ and $\lambda+\alpha$…