8 problems

Let $A$ be an Auslander-Gorenstein Nakayama algebra, let $S$ be a simple $A$-module, and let $i$ be an odd integer. Odd-degree Ext dimension conjecture. One should have … The conje…

Let $A$ be an algebra with iso-class of simple modules $\mathcal{S}$, where $|\mathcal{S}|=n$. A total ordering on $\mathcal{S}$ is a $q$-ordering if every Weyl module is Schurian…

Fuchsian-category conjecture. The following properties hold:

Fuchsian-type conjecture. The following three statements hold:

Let $n\geq 2$ and let $k$ satisfy $2\leq k\leq 2n-2$. A Nakayama algebra is a finite-dimensional algebra whose indecomposable modules are uniserial; it is connected when its underl…

Let $n\geq 2$ and let $k$ satisfy $2\leq k\leq 2n-2$. A connected Nakayama algebra is a connected finite-dimensional Nakayama algebra, and $\operatorname{gldim}(A)$ denotes its glo…

Let $n$ and $r$ be integers with $2\leq r\leq 2n-2$. Consider Nakayama algebras with $n$ simple modules and global dimension $r$. Existence conjecture. For every such $n$ and $r$,…

Abrar's conjecture.