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Algebraic equivalence of cycles and algebraic models of smooth manifolds

Published online by Cambridge University Press:  04 December 2007

W. Kucharz
W. Kucharz
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, [email protected] Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141, USA
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Abstract

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On a real algebraic variety there may exist an algebraic cycle that is algebraically equivalent to zero and whose cohomology class is non-zero. The group of such cohomology classes can be highly non-trivial. It is interesting since it allows one to detect cohomology classes, in complementary dimension, which cannot be represented by algebraic cycles.

Keywords

real algebraic varietyalgebraic cyclecohomology class14P2514C25
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 501 - 510
Copyright
Foundation Compositio Mathematica 2004