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We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to its coarse moduli space and on representable morphisms.
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Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov–Witten theory of Deligne–Mumford stacks , arXiv.math.AG/0603151 (2006), 57
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M. J. Souto Salorio L. Alonso Tarrío, A. Jeremías López, Localization in categories of complexes and unbounded resolutions , Canadian Math. J. 52
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Gérard Laumon and Laurent Moret-Bailly, Champs algébriques , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 39, Springer-Verlag, Berlin, 2000
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Dan Edidin, Brendan Hassett, Andrew Kresch, and Angelo Vistoli, Brauer groups and quotient stacks , Amer. J. Math. 123
2001
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Martin Olsson and Jason Starr, Quot functors for deligne-mumford stacks , Comm. Algebra 31
2003
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2005
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