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We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks.
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K. Behrend, Derived l l -adic categories for algebraic stacks , Mem. Amer. Math. Soc. 163
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A. J. de Jong, A result of Gabber , preprint available at http://www.math.columbia.edu/~dejong/ , 2003, p. 9
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M. Lieblich, Moduli of twisted sheaves and generalized Azumaya algebras , ProQuest LLC, Ann Arbor, MI, 2004, Thesis (Ph.D.)–Massachusetts Institute of Technology
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J. Lurie, Tannaka duality for geometric stacks , preprint, December 2004, arXiv:math/0412266 , p. 14
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B. Totaro, The resolution property for schemes and stacks , J. Reine Angew. Math. 577
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V. Drinfeld and D. Gaitsgory, On some finiteness questions for algebraic stacks , Geom. Funct. Anal. 23
2013
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2014
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B. Antieau, A local-global principle for the telescope conjecture , Adv. Math. 254
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M. Brandenburg, Tensor categorical foundations of algebraic geometry , Ph.D. thesis, Wilhelms-Universität Münster, May 2014, p. 243
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J. Hall, Cohomology and base change for algebraic stacks , Math. Z. 278
2014
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M. Kashiwara and P. Schapira, Categories and sheaves , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 332, Springer-Verlag, Berlin, 2006
2006
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J. Lipman and A. Neeman, Quasi-perfect scheme-maps and boundedness of the twisted inverse image functor , Illinois J. Math. 51
2007
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M. Olsson, Sheaves on Artin stacks , J. Reine Angew. Math. 603
2007
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B. Toën and G. Vezzosi, Homotopical algebraic geometry. II. Geometric stacks and applications , Mem. Amer. Math. Soc. 193
2008
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Y. Laszlo and M. Olsson, The six operations for sheaves on Artin stacks. I. Finite coefficients , Publ. Math. Inst. Hautes Études Sci. (2008), no. 107, 109–168
2008
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J. Lurie, Higher topos theory , Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ, 2009
2009
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A. Krishna, Perfect complexes on Deligne-Mumford stacks and applications , J. K-Theory 4
2009
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