3 problems

Let $k$ be an algebraically closed field. Consider $k$-linear $\operatorname{Ext}$-finite hereditary categories satisfying Serre duality, and regard two such categories as equivale…

Classification conjecture. There are no other such hereditary categories ${\cal C}$.

Let $\mathcal A$ and $\mathcal B$ be hereditary abelian categories. Their root categories are the orbit categories $\mathcal D^b(\mathcal A)/[2]$ and $\mathcal D^b(\mathcal B)/[2]$…