For smooth, separated, quasi-DM stacks over a regular affine scheme, the diagonal dimension is bounded by a formula in dim R, dim U, and cd(Y); for varieties with mild singularities it is at most 2·dim X.
Neeman, Triangulated categories with a single compact generator an d a Brown repre- sentability theorem, preprint (2018)
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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
For smooth, separated, quasi-DM stacks over a regular affine scheme, the diagonal dimension is bounded by a formula in dim R, dim U, and cd(Y); for varieties with mild singularities it is at most 2·dim X.
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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.