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arXiv · 1311.5538

An approach to intersection theory on singular varieties using motivic complexes

Eric M. Friedlander·Joseph Ross
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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 upon 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.

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BibTeXRIS

Eric M. Friedlander, Joseph Ross. 2016-05-20. An approach to intersection theory on singular varieties using motivic complexes. https://doi.org/10.1112/s0010437x16007697

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