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An approach to intersection theory on singular varieties using motivic complexes

Eric M. Friedlander, J. Ross
2016 Compositio Mathematica  
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
more » ... pairings on equivalence classes. We establish suspension and splitting theorems, as well as a localization property. Some examples of intersections on singular varieties are computed.
doi:10.1112/s0010437x16007697 fatcat:n3756dhprzhr5hqo7vvmzadsxq