An approach to intersection theory on singular varieties using motivic complexes Article Swipe

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Mathematics Intersection homology Intersection theory Pure mathematics Cohomology Equivalence (formal languages) Homology (biology) Intersection (aeronautics) Motivic cohomology Equivalence relation Complete intersection Algebra over a field Mathematical analysis De Rham cohomology Equivariant cohomology Differential equation Chemistry Aerospace engineering Differential algebraic equation Engineering Ordinary differential equation Gene Biochemistry

Eric M. Friedlander , Joseph S. Ross ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1112/s0010437x16007697 · OA: W1543777889

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.