Cohomological descent theory for a morphism of stacks and for equivariant derived categories

Details Cohomological descent theory for a morphism of stacks and for equivariant derived categories Cohomological descent theory for a morphism of stacks and for equivariant derived categories

2011-03-16

arxiv.org/abs/1103.3135v1

Mathematics

Algebraic Geometry

28 pages

Scientific paper

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, we show that for an action of a reductive group on a scheme, the derived category of equivariant sheaves is equivalent to the category of objects, equipped with an action of the group, in the ordinary derived category.

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