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Volume 1, Issue 1

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

Pages: 14 – 29


Yong Liu and Donald Stanley


We study the nullity classes in the full triangulated subcategory \(D^{cof}_{fg}(R)\) of the derived category \(D(R)\), where \(R\) is a commutative noetherian ring of finite Krull dimension. In this subcategory \(D^{cof}_{fg}(R)\), every object can be represented by a cofibrant complex of finitely generated \(R\)-modules. Using the perversity functions, we obtain a complete invariant of nullity classes in \(D^{cof}_{fg}(R)\), which classifies the aisles, or equivalently, the \(t\)-structures in the same category.

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Received: 2 June 2019; Accepted: 18 June 2019.