9 problems

Happel–Unger conjecture. The graph $\mathcal{G}(\mathcal{T}_{\mathbb{X}})$ is connected.

Let $\mathcal{C}_1$ and $\mathcal{C}_2$ be finitary hereditary connected $\mathbb{F}_q$-linear categories, and let $\widetilde{\mathbf{D}}\mathbf{H}_{\mathcal{C}_i}$ denote their r…

Let $\mathbb{X}_{\mathbf{p},\underline{\lambda}}$ be a weighted projective line, let $\mathfrak{Lg}$ be its corresponding loop Kac–Moody algebra, and use the identification…

Let $\mathbb{X}$ be a weighted projective line and let $T$ be a tilting complex of the form … with $T_i\in\operatorname{coh}(\mathbb{X})$, $T_0\neq 0\neq T_m$, and…

HRS-tilt characterization conjecture. The aisle $cD^{\leq 0}$ contains no nonzero Ext-projective if and only if it is a shift of the HRS-tilt associated with some torsion pair…

Derived-equivalence conjecture. Given an arbitrary weighted projective line $cX$, Assertion holds for $cD=\mathcal{D}^b(cX)$.

Let $\mathbb{X}$ be a weighted projective line of minimal wild weight type $(2,3,7)$, and let $F$ be an exceptional object in $\underline{\operatorname{vect}}\textrm{-}\mathbb{X}$.…

Let $\mathbb{X}$ be a weighted projective line of weight type $(2,a,b)$ with $a,b\geq4$. A tilting object in $\underline{\operatorname{vect}}\textrm{-}\mathbb{X}$ is a tilting obje…

Density conjecture. For $p\geq 7$, the above embedding is not dense. This concerns the comparison between the orbit category arising from the grading shift and the category associa…