Inequalities bound homological dimensions across recollements in triangulated categories, extending ring-theoretic finiteness results.
Localization theorems for weakly approximable triangulated categories
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abstract
Weakly approximable triangulated categories, introduced by Neeman, provide a powerful framework for studying localization phenomena in triangulated categories. In this paper, we establish new localization theorems showing that, under mild assumptions, a recollement of weakly approximable triangulated categories induces short exact sequences on several natural triangulated subcategories as well as on the associated (big) singularity categories. As applications, we illustrate our results in the derived categories of rings, DG algebras, and schemes.
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2026 1verdicts
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Finiteness of homological dimensions in triangulated categories
Inequalities bound homological dimensions across recollements in triangulated categories, extending ring-theoretic finiteness results.