Descent theory for semiorthogonal decompositions

الأصل · EN

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.