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An approach to intersection theory on singular varieties using motivic complexes

Published online by Cambridge University Press:  08 November 2016

Eric M. Friedlander
Affiliation:
University of Southern California, Department of Mathematics, 3620 South Vermont Avenue KAP 104, Los Angeles, CA 90089, USA email [email protected], [email protected]
J. Ross
Affiliation:
University of Southern California, Department of Mathematics, 3620 South Vermont Avenue KAP 104, Los Angeles, CA 90089, USA email [email protected]

Abstract

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 equivalence classes. We establish suspension and splitting theorems, as well as a localization property. Some examples of intersections on singular varieties are computed.

Type
Research Article
Copyright
© The Authors 2016 

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