5 problems

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…

Let $R$ be a local $k$-algebra such that the $R$-module of $k$-derivations $\operatorname{Der}_k(R)$ is finitely generated. Write $\operatorname{Gdim}$ for Gorenstein dimension and…

For an Artin algebra, the -dimension is an upper bound on its finitistic dimension. The -dimension conjecture. This upper bound is always finite. If true, this would imply the fini…

Finitistic-dimension conjecture. The big finitistic dimension satisfies

Let $R$ be the ring under consideration, let $C$ be a semidualizing module, and let $X$ be any $R$-module. Write $\mathcal{G}_C\mathop{\rm \text{-}dim}\nolimits X$ and…