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• W3116248049 abstract "Abstract Let $R$ be a commutative noetherian ring. The notion of $n$-wide subcategories of ${operatorname{mathsf{Mod}}} R$ is introduced and studied in Matsui–Nam–Takahashi–Tri–Yen in relation to the cohomological dimension of a specialization-closed subset of ${operatorname{Spec}} R$. In this paper, we introduce the notions of $n$-coherent subsets of ${operatorname{Spec}} R$ and $n$-uniform subcategories of $mathsf{D}({operatorname{mathsf{Mod}}} R)$ and explore their interactions with $n$-wide subcategories of ${operatorname{mathsf{Mod}}} R$. We obtain a commutative diagram that yields filtrations of subcategories of ${operatorname{mathsf{Mod}}} R$, $mathsf{D}({operatorname{mathsf{Mod}}} R)$ and subsets of ${operatorname{Spec}} R$ and complements classification theorems of subcategories due to Gabriel, Krause, Neeman, Takahashi, and Angeleri Hügel–Marks–Šťovíček–Takahashi–Vitória." @default.
• W3116248049 created "2021-01-05" @default.
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• W3116248049 date "2020-12-28" @default.
• W3116248049 modified "2023-10-16" @default.
• W3116248049 title "Filtrations in Module Categories, Derived Categories, and Prime Spectra" @default.
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• W3116248049 doi "https://doi.org/10.1093/imrn/rnaa284" @default.
• W3116248049 hasPublicationYear "2020" @default.
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