• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Descent theory for semiorthogonal decompositions

Sbornik Mathematics. 2012. Vol. 203. No. 5. P. 645-676.

We put forward a method for constructing semiorthogonal decompositions of the derived category of G-equivariant sheaves on a variety X under the assumption that the derived category of sheaves on X admits a semiorthogonal decomposition with components preserved by the action of the group G on X. This method is used to obtain semiorthogonal decompositions of equivariant derived categories for projective bundles and blow-ups with a smooth centre as well as for varieties with a full exceptional collection preserved by the group action. Our main technical tool is descent theory for derived categories.