A theory of algebraic cocycles
Abstract
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an EilenbergMacLane 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 $L$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 $(p,p)$cohomology class.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 1992
 arXiv:
 arXiv:math/9204230
 Bibcode:
 1992math......4230F
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 5 pages