8 problems

Arbitrary type $A_n$ quiver conjecture. The results should hold, with similar proofs, when the quiver is replaced by an arbitrary Dynkin quiver of type $A_n$; in this general case,…

Let $Q$ be a quiver whose underlying unoriented graph is a disjoint union of Dynkin diagrams of type $A$, $D$, or $E$. A representation of $Q$ is called stable with respect to a we…

Let $\Gamma$ be a Dynkin quiver, let $Y$ be the associated representation variety, and let $\pi:X\to Y$ be the map whose fibres are flag versions of quiver Grassmannians. For a fie…

Let $Q$ be a Dynkin quiver, and let $k$ be the field over which its representations are taken. Write $\mathrm{\mathbf{Rep}}_k(Q)$ for the abelian category of finite-dimensional $k$…

Let $Q$ be a quiver of Dynkin type. A weight system $\Theta$ on $Q$ is understood in the sense of stability for representations of $Q$, and a representation is stable with respect…

Let $Q$ be a Dynkin quiver, let $M$ be a representation of $Q$, and let $Gr_{\mathbf{e}}(M)$ be the associated quiver Grassmannian. A cellular decomposition means an $\alpha$-parti…

Let $M$ be a representation of a Dynkin quiver and let $Gr_{\mathbf{e}}(M)$ denote its quiver Grassmannian of subrepresentations with dimension vector $\mathbf{e}$. Property (textb…

Let $\Gamma$ be a quiver and let $\mathbf{k}$ be a field. Call $\Gamma$ $\mathbf{k}$-even if the complexes $\pi_{y*}\underline{\mathbf{k}}_{\widetilde{F}_{y}}$ are even for every…