9 problems

Let $A$ be a properly stratified algebra with a simple preserving duality. Write $\fdim(A)$ for its finitistic dimension, $\fdim_{\Delta}(A)$ for its Delta-finitistic dimension, an…

Let $\Lambda$ be an algebra. The derived delooping–finitistic dimension conjecture. … This conjectures that the derived delooping level of $\Lambda$ equals the finitistic dimension…

Big finitistic dimension conjecture. If $A$ is an Artin algebra, then

Second Finitistic Dimension Conjecture. The small finitistic dimension is finite:

Small finitistic dimension conjecture. The finitistic dimension is finite:

Mazorchuk–Parker's conjecture. The finitistic dimension of $A$ is equal to two times the projective dimension of its characteristic tilting module:

Finitistic dimension conjecture. There exists a uniform bound on the projective dimensions of all finitely generated left $A$-modules of finite projective dimension.

Let $A$ be an Artin algebra, and let $M$ range over finitely generated $A$-modules of finite projective dimension. The finitistic dimension conjecture. The quantity … is finite. Th…

Finitistic dimension conjecture. Every Artin algebra has finite finitistic dimension.