A theory of algebraic cocycles
Algebraic Geometry
2016-09-06 v1
Abstract
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial, and admits Gysin maps. It carries a natural cup product and a pairing to -homology. Chern classes of algebraic bundles are defined in the theory. There is a natural transformation to (singular) integral cohomology theory that preserves cup products. Computations in special cases are carried out. On a smooth variety it is proved that there are algebraic cocycles in each algebraic rational -cohomology class.
Cite
@article{arxiv.math/9204230,
title = {A theory of algebraic cocycles},
author = {Eric M. Friedlander and H. Blaine Lawson},
journal= {arXiv preprint arXiv:math/9204230},
year = {2016}
}
Comments
5 pages