8 problems

Throughout, let $R$ be a commutative ring with identity, let $S\subset R$ be a multiplicative subset, and let $R_S$ denote the localization of $R$ with respect to $S$. An $R$-modul…

Telescope Conjecture for module categories. Every such cotorsion pair is of finite type.

Relative flaprojective periodicity conjecture. The $A$-modules of cocycles of $F^\bullet$ are $A/R$-flaprojective.

Let $R$ be a commutative ring and let $S$ be a finitely presented flat commutative $R$-algebra. A commutative ring homomorphism $R\to S$ is very flat when, for every element…

Countable Telescope Conjecture for module categories. The cotorsion pair $(\mathcal{A},\mathcal{B})$ is of countable type.

Let $\mathcal{C}$ be an indecomposable $2$-Calabi–Yau triangulated category, and let $\mathscr{M}(\mathcal{C})$ be the quiver whose vertices are cotorsion pairs in $\mathcal{C}$, w…

Let $\Lambda$ be an artin algebra, and let $(\mathcal{A},\mathcal{B})$ be a hereditary cotorsion pair in the category of all left $\Lambda$-modules. A cotorsion pair is of finite t…

Let $Lambda$ be an artin algebra, and let $(\mathcal{A},\mathcal{B})$ be a hereditary cotorsion pair in the category of all left $Lambda$-modules. A cotorsion pair is hereditary wh…