Descent theory for semiorthogonal decompositions

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.

33 pages

References in corpus (1)

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

Cited by in corpus (3)

• Derived categories of cyclic covers and their branch divisors
• Group actions on categories and Elagin's Theorem Revisited
• A note on equivariantization of additive categories and triangulated categories