The Stacks project

112.5.5 Cohomology

Papers discussing cohomology of sheaves on algebraic stacks.

  • Olsson: Sheaves on Artin stacks [olsson_sheaves]

    This paper develops the theory of quasi-coherent and constructible sheaves proving basic cohomological properties. This paper corrects a mistake in [LM-B] in the functoriality of the lisse-étale site. The cotangent complex is constructed. In addition, the following theorems are proved: Grothendieck's Fundamental Theorem for proper morphisms, Grothendieck's Existence Theorem, Zariski's Connectedness Theorem and finiteness theorem for proper pushforwards of coherent and constructible sheaves.

  • Behrend: Derived $l$-adic categories for algebraic stacks [behrend_derived]

    Proves the Lefschetz trace formula for algebraic stacks.

  • Behrend: Cohomology of stacks [behrend_cohomology]

    Defines the de Rham cohomology for differentiable stacks and singular cohomology for topological stacks.

  • Faltings: Finiteness of coherent cohomology for proper fppf stacks [faltings_finiteness]

    Proves coherence for direct images of coherent sheaves for proper morphisms.

  • Abramovich, Corti, Vistoli: Twisted bundles and admissible covers [acv]

    The appendix contains the proper base change theorem for étale cohomology for tame Deligne-Mumford stacks.

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