An approach to intersection theory on singular varieties using motivic complexes. (8th November 2016)

• Record Type: Journal Article
• Authors: Friedlander, Eric M.; Ross, J.
• Is Part Of: Compositio mathematica. Volume 152:Number 11(2016)
• Page Start: 2371
• Page End: 2404
• Publication Date: 2016-11-08
• Subjects: 14F43, -- 14C25, -- 19E15 (primary); intersection homology, -- perversity, -- cocycles, -- cycle complexes; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007697
• Languages: English
• ISSNs: 0010-437X

Abstract

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 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.