Linearisations of triangulated categories with respect to finite group actions

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

2011-08-10

arxiv.org/abs/1108.2144v1

Mathematics

Algebraic Geometry

14 pages; comments welcome

Scientific paper

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.

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