Diagonal dimension of a variety with mild singularities is at most twice its Krull dimension; explicit upper bounds are given for smooth morphisms to regular targets.
Neeman, Triangulated categories with a single compact generator an d a Brown repre- sentability theorem, preprint (2018), arXiv:1804.02240
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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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Remarks on diagonal dimension for algebraic stacks
Diagonal dimension of a variety with mild singularities is at most twice its Krull dimension; explicit upper bounds are given for smooth morphisms to regular targets.
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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.