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arXiv · 2608.14255

Torsion pairs in subcategories of modules over a commutative ring

Shinnosuke Kosaka·Ryo Takahashi·Gen Tanigawa
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Abstract

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

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Shinnosuke Kosaka, Ryo Takahashi, Gen Tanigawa. 2026-08-14. Torsion pairs in subcategories of modules over a commutative ring. https://arxiv.org/abs/2608.14255

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