Cohomological descent theory for a~morphism of stacks and for equivariant derived categories
Sbornik. Mathematics, Tome 202 (2011) no. 4, pp. 495-526
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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.
@article{SM_2011_202_4_a1,
author = {A. Elagin},
title = {Cohomological descent theory for a~morphism of stacks and for equivariant derived categories},
journal = {Sbornik. Mathematics},
pages = {495--526},
publisher = {mathdoc},
volume = {202},
number = {4},
year = {2011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2011_202_4_a1/}
}
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/