5 problems

Dimension conjecture. If $R$ has countable $\operatorname{CM}$-representation type, then

Hypersurface conjecture. If $R$ has countable $\operatorname{CM}$-representation type, then $R$ is a hypersurface.

Finite-plus/countable representation type conjecture. The following conditions are equivalent:

Let $(R,\mathbb{L})$ be a Geigle–Lenzing complete intersection, let $d$ be the dimension parameter, and let $A^{\rm CM}$ be its CM endomorphism algebra. A $d$-tilting object is an…

Let $(R,\mathbb{L})$ be a Geigle–Lenzing complete intersection, with canonical element $\vec{\omega}\in\mathbb{L}$, and let $d$ be the relevant dimension parameter. The pair…