Localization theorems for weakly approximable triangulated categories
Representation Theory
2026-04-14 v3 Category Theory
Rings and Algebras
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.
Cite
@article{arxiv.2402.04954,
title = {Localization theorems for weakly approximable triangulated categories},
author = {Yongliang Sun and Jinbi Zhang and Yaohua Zhang},
journal= {arXiv preprint arXiv:2402.04954},
year = {2026}
}
Comments
33 pages. Correct some minor errors. Comments are welcome