Article

Descent theory for semiorthogonal decompositions

06/2012;
Source: arXiv

ABSTRACT In this paper a method of constructing a semiorthogonal decomposition of the
derived category of $G$-equivariant sheaves on a variety $X$ is described,
provided that the derived category of sheaves on $X$ admits a semiorthogonal
decomposition, whose components are preserved by the action of the group $G$ on
$X$. Using this method, semiorthogonal decompositions of equivariant derived
categories were obtained for projective bundles and for blow-ups with a smooth
center, and also for varieties with a full exceptional collection, preserved by
the action of the group. As a main technical instrument, descent theory for
derived categories is used.

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Keywords

$G$-equivariant sheaves
 
categories
 
components
 
derived category
 
descent theory
 
group $G$
 
main technical instrument
 
projective bundles
 
semiorthogonal decomposition
 
semiorthogonal decompositions
 
sheaves
 
varieties
 
variety $X$