Torsion pairs in subcategories of modules over a commutative ring

Abstract

Let $R$ be a commutative noetherian ring. Denote by $\mathrm{mod}R$ the category of finitely generated $R$-modules. Let $\Delta$ be a subset of $\mathrm{Spec}R$, and let ${\mathrm{Ass}}^{-1}\Delta$ stand for the full subcategory of $\mathrm{mod}R$ consisting of finitely generated $R$-modules whose associated prime ideals belong to $\Delta$. In this paper, we consider classifying torsion pairs in ${\mathrm{Ass}}^{-1}\Delta$ and some other full subcategories of $\mathrm{mod}R$.

arXiv comment14 pages