5 problems

Let $G$ be a group and let $k$ be a commutative ring of finite global dimension. Write ${\tt Cof}(kG)$ for the class of cofibrant $kG$-modules and ${\tt GProj}(kG)$ for the class o…

Let $A$ be an Artin algebra and let $M$ be a finitely generated Gorenstein projective module, meaning that $M$ is Gorenstein projective over $A$. Gorenstein projective conjecture.…

Let $D$ be a connected Postnikov diagram with ice quiver $(Q_D,F_D)$, potential $W_D$, dimer algebra $A_D$, and boundary idempotent $e$. Set $B_D=eA_De$, and let…

Let $A$ and $B$ be finite-dimensional $k$-algebras, and set … An algebra is CM-free when its finitely generated Gorenstein-projective modules are precisely its projective modules,…

Finite-dimension conjecture. Every module $M$ satisfying ${\rm Gpd}(M)<\infty$ and ${\rm fd}(M)<\infty$ also satisfies