Classifying preaisles of derived categories of complete intersections

Abstract

Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod}R$ the category of finitely generated $R$-modules, by $\operatorname{D^b}(R)$ the bounded derived category of $\operatorname{mod}R$, and by $\operatorname{D_{sg}}(R)$ the singularity category of $R$. The main result of this paper provides, when $R$ is a complete intersection, a complete classification of the preaisles of $\operatorname{D^b}(R)$ containing $R$ and closed under direct summands, which includes as restrictions the classification of thick subcategories of $\operatorname{D_{sg}}(R)$ due to Stevenson, and the classification of resolving subcategories of $\operatorname{mod}R$ due to Dao and Takahashi.