Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.
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Proves that recollements of weakly approximable triangulated categories induce short exact sequences on triangulated subcategories and associated big singularity categories under mild assumptions, with applications to derived categories of rings, DG algebras, and schemes.
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Homological Aspects of Separable Extensions of Triangulated Categories
Separable extensions preserve finiteness of global dimension, Gorensteinness and regularity in compactly generated triangulated categories while relating their singularity categories up to retracts.
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Localization theorems for weakly approximable triangulated categories
Proves that recollements of weakly approximable triangulated categories induce short exact sequences on triangulated subcategories and associated big singularity categories under mild assumptions, with applications to derived categories of rings, DG algebras, and schemes.