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arXiv · 1912.10584

Filtrations in module categories, derived categories and prime spectra

Hiroki Matsui·Ryo Takahashi
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Abstract

Let R be a commutative noetherian ring. The notion of n-wide subcategories of Mod R is introduced and studied in Matsui-Nam-Takahashi-Tri-Yen in relation to the cohomological dimension of a specialization-closed subset of Spec R. In this paper, we introduce the notions of n-coherent subsets of Spec R and n-uniform subcategories of D(Mod R), and explore their interactions with n-wide subcategories of Mod R. We obtain a commutative diagram which yields filtrations of subcategories of Mod R, D(Mod R) and subsets of Spec R and complements classification theorems of subcategories due to Gabriel, Krause, Neeman, Takahashi and Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria.

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Hiroki Matsui, Ryo Takahashi. 2020-09-25. Filtrations in module categories, derived categories and prime spectra. https://arxiv.org/abs/1912.10584

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