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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



A theory of algebraic cocycles

Authors: Eric M. Friedlander and H. Blaine Lawson
Journal: Bull. Amer. Math. Soc. 26 (1992), 264-268
MSC (2000): Primary 14C05; Secondary 14C30, 14F35
MathSciNet review: 1118701
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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 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.

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Keywords: Algebraic cycle, Chow variety, algebraic cocycle, cohomology
Article copyright: © Copyright 1992 American Mathematical Society

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