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

Yong Liu; Donald Stanley

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arXiv · 1610.09523

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

Yong Liu·Donald Stanley

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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 $D^c_{fg}(R)$.

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Yong Liu, Donald Stanley. 2016-10-29. A classification of nullity classes in the derived category of a ring. https://arxiv.org/abs/1610.09523

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