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# Mathematical Research Letters

## Volume 19 (2012)

### Number 5

### Linearisations of triangulated categories with respect to finite group actions

Pages: 1007 – 1020

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n5.a4

#### Author

#### Abstract

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.

#### Keywords

triangulated categories, autoequivalences, enhancements, linearizations

#### 2010 Mathematics Subject Classification

14F05, 18E30