Jardine: Fibred sites and stack cohomologyopology/0406483)
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AG (Algebraic geometry)
Stacks
Where does this belong? arXiv:1101.2918 Cohomology with coefficients in stacks of Picard categories from arXiv Front: math.AT by Mamuka Jibladze, Teimuraz Pirashvili Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and the Ext groups of appropriate stacks.
Martin Olsson: I will discuss recent joint work with Yves Laszlo generalizing Grothendieck’s six operations to Artin stacks. In the development of these operations a number of interesting technical issues present themselves which I will discuss in the talk. For example, morphisms of algebraic stacks are usually not compactifiable and do not have bounded cohomology. Also for applications to geometric Langland’s program it is important to consider stacks which are not quasi-compact. I will explain how we overcome these difficulties in both the cases of finite and adic coefficients.
nLab page on Stack cohomology