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An approach to intersection theory on singular varieties using motivic complexes

Part of: Cycles and subschemes $K$-theory in geometry (Co)homology theory

Published online by Cambridge University Press:  08 November 2016

Eric M. Friedlander  and
J. Ross
Eric M. Friedlander
Affiliation:
University of Southern California, Department of Mathematics, 3620 South Vermont Avenue KAP 104, Los Angeles, CA 90089, USA email ericmf@usc.edu, eric@math.northwestern.edu
J. Ross
Affiliation:
University of Southern California, Department of Mathematics, 3620 South Vermont Avenue KAP 104, Los Angeles, CA 90089, USA email joseph.ross@gmail.com
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Abstract

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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.

Keywords

intersection homologyperversitycocyclescycle complexes

MSC classification

Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14C25: Algebraic cycles 19E15: Algebraic cycles and motivic cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 11 , November 2016 , pp. 2371 - 2404
Copyright
© The Authors 2016 

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