An approach to intersection theory on singular varieties using motivic complexes

@article{Friedlander2016AnAT,
  title={An approach to intersection theory on singular varieties using motivic complexes},
  author={E. Friedlander and J. Ross},
  journal={Compositio Mathematica},
  year={2016},
  volume={152},
  pages={2371 - 2404}
}
We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky–MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity homology theory and a companion perversity cohomology theory based on generalized cocycle spaces. These theories lead to conditions on pairs of cycles which can be intersected and a suitable equivalence relation on cocycles/cycles enabling pairings on… Expand
Intersections via resolutions
Noncommutative resolutions and intersection cohomology for quotient singularities
Intersection K-theory

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