8 problems

Lattice-isomorphism conjecture. These lattices are isomorphic, compatibly with the identification predicted by the periodicity conjecture for the corresponding Grothendieck-group c…

For a commutative ring $A$, let $A\textrm{-}\mathcal{CAT}^{Mor}$ denote the Morita localization of linear categories and let $A\textrm{-}\mathcal{AB}^{proj}$ be the subcategory of…

Let $X$ be an algebraic variety over $\mathbb{Q}$. An object $M$ of the abelian category $\mathcal{M}_\mathrm{univ}(X,\mathbb{Z})$ is torsion-free if multiplication by every nonzer…

Axiomatization conjecture for extended directories. Then $D$ is an extended directory: there is an object $A$ in a $K_0$-linear abelian category such that

Let $\mathsf B$ be a locally presentable abelian category with a projective generator $P$. Let $\mathsf B_{\operatorname{proj}}$ denote the class of projective objects in…

Red-path realization conjecture. Every maximal green sequence in $\mathcal{A}$ is induced by a red path in the wall and chamber structure of $\mathcal{A}$.

Hereditary abelian subcategory conjecture. The category $\mathcal C'$ is a $\operatorname{Hom}$-finite hereditary abelian category.

Global-dimension extension. This is true for all Abelian categories with coproducts.