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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.

References [Enhancements On Off] (What's this?)

  • [F] E. Friedlander, Algebraic cycles, Chow varieties, and Lawson homology, Compositio Math. 77 (1991), 55-93. MR 1091892 (92a:14005)
  • [FL] E. Friedlander and H. B. Lawson, A theory of algebraic cocycles, Ann. of Math. (to appear).
  • [FM] E. Friedlander and B. Mazur, Filtrations on the homology of algebraic varieties (to appear). MR 1211371 (95a:14023)
  • [L-F1] P. Lima-Filho, On a homology theory for algebraic varieties, IAS preprint, 1990.
  • [L-F2] -, Completions and fibrations for topological monoids and excision for Lawson homology, Compositio Math., (1991).
  • [L] H. B. Lawson, Jr., Algebraic cycles and homotopy theory, Ann. of Math. (2) 129 (1989), 253-291. MR 986794 (90h:14008)
  • [LM] H. B. Lawson, Jr. and M.-L. Michelsohn, Algebraic cycles, Bott periodicity, and the Chern characteristic map, The Mathematical Heritage of Herman Weyl, Amer. Math. Soc., Providence, RI, 1988, pp. 241-264. MR 974339 (90d:14010)

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

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