Classifying localizing subcategories of a locally coherent category

2025/07/18 by Reza Sazeedeh, Sazeedeh, Reza
Mathematics · #13C05 #18E10 #18E35 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.13749

openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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