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arXiv · 2402.04954

Localization theorems for weakly approximable triangulated categories

Yongliang Sun·Jinbi Zhang·Yaohua Zhang
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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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Yongliang Sun, Jinbi Zhang, Yaohua Zhang. 2026-04-13. Localization theorems for weakly approximable triangulated categories. https://arxiv.org/abs/2402.04954

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