An approach to intersection theory on singular varieties using motivic complexes

作者：Friedlander Eric M^*; Ross J

来源：Compositio Mathematica, 2016, 152(11): 2371-2404.

DOI：10.1112/S0010437X16007697

• intersection homology
• perversity
• cocycles
• cycle complexes

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.

• 出版日期2016-11