3 problems

Let $\mathcal{A}$ be an Ext-finite abelian category with Serre duality, and let $(\mathcal{T},\mathcal{F})$ be a torsion pair on $\mathcal{A}$. Denote by $U_{\mathcal{T}}$ the aisl…

HRS-tilt characterization conjecture. The aisle $cD^{\leq 0}$ contains no nonzero Ext-projective if and only if it is a shift of the HRS-tilt associated with some torsion pair…

Let $(\mathcal{T},\mathcal{F})$ be an elementary torsion pair in $\operatorname{Mod}\textrm{-}{R}$, where $R$ is a ring. The torsion class $\mathcal{T}$ is said to have enough pure…