Geodesic
Cohomological descent theory for a morphism of stacks and for equivariant derived categories
Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 495-526 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, we find necessary and sufficient conditions under which, if $X\to S$ is a morphism of algebraic varieties (or, in a more general case, of stacks), the derived category of $S$ can be recovered by using the tools of descent theory from the derived category of $X$. We show that for an action of a linearly reductive algebraic group $G$ on a scheme $X$ this result implies the equivalence of the derived category of $G$-equivariant sheaves on $X$ and the category of objects in the derived category of sheaves on $X$ with a given action of $G$ on each object. Bibliography: 18 titles.
Keywords: derived categories, descent theory, algebraic variety. 
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     title = {Cohomological descent theory for a~morphism of stacks and for equivariant derived categories},
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A. Elagin. Cohomological descent theory for a morphism of stacks and for equivariant derived categories. Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 495-526. http://geodesic.mathdoc.fr/item/SM_2011_202_4_a1/

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