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.
A generalized Bondal–Orlov full faithfulness criterion for Deligne– Mumford stacks
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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.