A classification of nullity classes in the derived category of a ring

Abstract

For a commutative Noetherian ring $R$ with finite Krull dimension, we study the nullity classes in $D^c_{fg}(R)$, the full triangulated subcategory $D^c_{fg}(R)$ of the derived category $D(R)$ consisting of objects which can be represented by cofibrant objects with each degree finitely generated. In the light of perversity functions over the prime spectrum $\mathrm{Spec} R$, we prove that there is a complete invariant of nullity classes thus that of aisles (or equivalently, $t$-structures) in $D^c_{fg}(R)$.