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Equivalences of derived categories of sheaves on tame stacks
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Building on Olander's work on algebraic spaces, we prove Orlov's representability theorem relating fully faithful functors and Fourier--Mukai transforms between the bounded derived category of coherent sheaves to the case of smooth, proper, and tame algebraic stacks. This extends previous results of Kawamata for Deligne--Mumford stacks with generically trivial stabilizers and projective coarse moduli spaces.
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Cited by 2 Pith papers
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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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Compact approximation and descent for algebraic stacks
Approximation by compact complexes holds for quasi-compact quasi-separated algebraic stacks with quasi-finite diagonal, and this property descends along quasi-finite flat covers.
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