Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Nonvanishing of external products for higher Chow groups


Authors: Andreas Rosenschon and Morihiko Saito
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 441-459
DOI: https://doi.org/10.1090/S1056-3911-03-00361-8
Published electronically: December 9, 2003
MathSciNet review: 2047676
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Abstract | References | Additional Information

Abstract: Consider an external product of a higher cycle and a usual cycle which is algebraically equivalent to zero. Assume there exists an algebraically closed subfield $k$ such that the higher cycle and its ambient variety are defined over $k$, but the image of the usual cycle by the Abel-Jacobi map is not. Then we prove that the external product is nonzero if the image of the higher cycle by the cycle map to the reduced Deligne cohomology does not vanish. We also give examples of indecomposable higher cycles on even-dimensional hypersurfaces of degree at least four in a projective space which satisfy the last condition.


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Additional Information

Andreas Rosenschon
Affiliation: Department of Mathematics, University at Buffalo, SUNY, Buffalo, NY 14260
Email: axr@buffalo.edu

Morihiko Saito
Affiliation: RIMS Kyoto University, Kyoto 606–8502, Japan
Email: msaito@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S1056-3911-03-00361-8
Received by editor(s): January 11, 2002
Published electronically: December 9, 2003

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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