Linearisations of triangulated categories with respect to finite group actions
arXiv:1108.2144 · doi:10.4310/MRL.2012.v19.n5.a4
Abstract
Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearised triangulated category using DG-enhancements. In particular, if the group is a finite group of automorphisms of a smooth projective variety and the category is the bounded derived category of coherent sheaves, then our construction produces the bounded derived category of coherent sheaves on the smooth quotient variety resp. stack. We also consider the action given by the tensor product with a torsion canonical bundle and the action of a finite group on the category generated by a spherical object.
14 pages; comments welcome
References in corpus (1)
Cited by in corpus (6)
- On equivariant triangulated categories
- Equivalences of equivariant derived categories
- Scalar extensions of triangulated categories
- Group actions on categories and Elagin's Theorem Revisited
- A note on equivariantization of additive categories and triangulated categories
- A power structure over the Grothendieck ring of geometric dg categories