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.
From: Reza Sazeedeh [view email]
[v1]
Fri, 18 Jul 2025 08:54:53 UTC (22 KB)
[v2]
Tue, 25 Nov 2025 14:54:02 UTC (19 KB)
[v3]
Tue, 9 Jun 2026 21:33:03 UTC (20 KB)
[v4]
Mon, 17 Aug 2026 23:09:42 UTC (20 KB)
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