An approach to intersection theory on singular varieties using motivic complexes
K-Theory and Homology
2019-02-20 v2
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.
Cite
@article{arxiv.1311.5538,
title = {An approach to intersection theory on singular varieties using motivic complexes},
author = {Eric M. Friedlander and Joseph Ross},
journal= {arXiv preprint arXiv:1311.5538},
year = {2019}
}
Comments
revised version, to appear in Compositio Mathematica