9 problems

Self-orthogonal $\tau$-tilting conjecture. If $T$ is a self-orthogonal $\tau$-tilting $A$-module, then $T$ is $1$-tilting.

The gentle arbor F-triangle conjecture. In $SC_t$, there exists a facet $C$ such that the $F$-triangle for $(SC_t,C)$ coincides with the $F$-triangle associated with the transmuted…

The support tau-tilting enumeration conjecture. The number of support-$\tau$-tilting objects for the gentle quiver-with-relations $G_t$ is equal to the number of elements of $P_t$.

Let $\Lambda$ be an algebra, let $n\geq m\geq 1$, let $M$ be a module in $\operatorname{mod}(\Lambda)$, and let $\Gamma_M$ be the algebra associated with $M$ in the paper. Assume t…

Let $\Lambda$ be an algebra, let $n\geq 1$, and let $M$ be a module in $\operatorname{mod}(\Lambda)$. The notation $c4_n$-tilting refers to the higher $c4$-tilting notion used in t…

Let $bb$ be an algebra, let $n\geq 1$, and let $M$ be a $c4_n$-tilting module in $\operatorname{mod}(bb)$. Write … A subcategory is preenveloping if every module admits a left appr…

Let $\Lambda$ be a finite-dimensional algebra. Let $\mathcal W\subseteq\mathsf{mod}\Lambda$ be a $\tau$-perpendicular subcategory of $\mathsf{mod}\Lambda$, and let…

Let $B$ be a 2-Calabi–Yau tilted algebra whose quiver satisfies the dimer-tree condition, and let $\tau_B$ denote the Auslander–Reiten translation in $\operatorname{mod}B$. Tau-rig…

Finite global dimension conjecture. The algebra $\operatorname{End}_A(T)$ has finite global dimension.