15 problems

Let $Y$ be a singular variety admitting crepant categorical resolutions, and call a categorical resolution indecomposable when it has no nontrivial decomposition in the relevant ca…

Let $Y$ be a singular variety, and let a categorical resolution of $Y$ correspond to a Lefschetz decomposition of $4D^b(\mathit{Z})4D$, where $\mathit{Z}$ is the exceptional diviso…

Let a categorical resolution be a categorical enhancement resolving a singularity, and let an admissible component mean a full subcategory included by an admissible embedding. Mini…

Let $X$ be a singular variety and consider suitably minimal categorical resolutions together with other sufficiently well-behaved categorical resolutions of $X$. Minimal-resolution…

Let $4pi_*:4\mathscr{C}4to D^b(X)$ be a categorical resolution with kernel $4ker(4pi_*)$, and suppose fair crepancy is the intermediate condition introduced in the paper, requiring…

NCCR categorical-resolution conjecture. Every NCCR of $R$ yields a strongly crepant categorical resolution of $X$.

A categorical crepant resolution is a crepant resolution of a singular space by a smooth or homologically smooth category, together with the relevant pullback functor. Kuznetsov's…

Let $C$ be the singular Coble cubic, let $W$ be the associated smooth variety, let $q^*W$ be its indicated $\mathbb{P}^1$-bundle, and let $\Gamma$ be the associated genus-$2$ curve…

Let $C$ be the Coble cubic associated with a congruence of lines in the nine-variable case. Let $\Gamma$ be the genus-$2$ curve appearing in the construction, let $q^*W$ be the ass…

Let $W$ be a vector space of dimension $m$, and let $\operatorname{Pf}(2k,W)$ denote the closure of the locus of bivectors in $\Lambda^2W$ of rank $2k$. Let…

Let $Y$ be a quasiprojective scheme. A categorical resolution of $Y$ is a smooth triangulated category $\mathcal{T}$ equipped with adjoint functors…

Drinfeld's conjecture. The DG enhancement of $D^b_{\operatorname{coh}}(\mathcal D_X)$ has a smooth categorical compactification.

Strongly crepant categorical resolution conjecture. The collection…

Let $X$ be a smooth projective variety. A minimal Lefschetz decomposition of $\D^b(X)$ is a Lefschetz decomposition whose first block is minimal under inclusion, and a categorical…

Let $X$ be a separated scheme of finite type over a field. A categorical resolution of $D(X)$ is a functor $D(X)\to D(A)$ induced by a smooth DG algebra $A$ and full and faithful o…