Orbifold Cohomology as Periodic Cyclic Homology

@inproceedings{Baranovsky2002OrbifoldCA,
  title={Orbifold Cohomology as Periodic Cyclic Homology},
  author={Vladimir Baranovsky},
  year={2002}
}
  • Vladimir Baranovsky
  • Published 2002
It known from the work of Feigin-Tsygan, Weibel and Keller that the cohomology groups of a smooth complex variety X can be recovered from (roughly speaking) its derived category of coherent sheaves. In this paper we show that for a finite group G acting on X the same procedure applied to G-equivariant sheaves gives the orbifold cohomology of X/G. As an application, in some cases we are able to obtain simple proofs of an additive isomorphism between the orbifold cohomology of X/G and the usual… CONTINUE READING