Mathematical Research Letters
Volume 19 (2012)
Linearisations of triangulated categories with respect to finite group actions
Pages: 1007 – 1020
Given an action of a finite group on a triangulated category, we investigate under which conditions one can construct a linearized triangulated category using DGenhancements. 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 or 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.
triangulated categories, autoequivalences, enhancements, linearizations
2010 Mathematics Subject Classification