On localizing subcategories of derived categories
Ryo Takahashi
TL;DR
This paper provides a unified framework for understanding localizing subcategories of derived categories of commutative noetherian rings through subsets of their spectra and module subcategories.
Contribution
It unifies existing theorems of Gabriel, Neeman, and Krause by interpreting localizing subcategories via spectral subsets and module categories.
Findings
Unified interpretation of localizing subcategories
Connection between spectral subsets and module subcategories
Generalization of previous theorems
Abstract
Let A be a commutative noetherian ring. In this paper, we interpret localizing subcategories of the derived category of A by using subsets of Spec A and subcategories of the category of A-modules. We unify theorems of Gabriel, Neeman and Krause.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra