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arXiv · 2507.13749

Classifying localizing subcategories of a locally coherent category

Reza Sazeedeh
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Abstract

Let $\cA$ be a locally coherent Grothendieck category, $\fp\cA$ be the full subcategory of $\cA$ consisting of finitely presented objects and $\ASpec\cA$ be the atom spectrum of $\cA$. In this paper, we classify localizing subcategories of finite type of $\cA$ via open subsets of $\ASpec\cA$. We investigate $\ASpec\fp\cA$ and show that if $\ASpec\fp\cA=\ASpec\cA$, then $\cA$ is locally noetherian. As an application, we specialize our investigation to the case of commutative coherent rings.

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Reza Sazeedeh. 2025-07-18. Classifying localizing subcategories of a locally coherent category. https://arxiv.org/abs/2507.13749

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