English

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.

Keywords

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

R2 v1 2026-06-22T02:12:24.777Z