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The Abel-Jacobi map for higher Chow groups

Kerr, M.; Lewis, J.; Mueller-Stach, S.

Authors

M. Kerr

J. Lewis

S. Mueller-Stach



Abstract

We construct a map between Bloch's higher Chow groups and Deligne homology for smooth, complex quasiprojective varieties on the level of complexes. For complex projective varieties this results in a formula which generalizes at the same time the classical Griffiths Abel–Jacobi map and the Borel/Beilinson/Goncharov regulator type maps.

Citation

Kerr, M., Lewis, J., & Mueller-Stach, S. (2006). The Abel-Jacobi map for higher Chow groups. Compositio Mathematica, 142(2), 374-396. https://doi.org/10.1112/s0010437x05001867

Journal Article Type Article
Publication Date Mar 1, 2006
Deposit Date Jan 8, 2008
Journal Compositio Mathematica
Print ISSN 0010-437X
Electronic ISSN 1570-5846
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 142
Issue 2
Pages 374-396
DOI https://doi.org/10.1112/s0010437x05001867
Keywords Abel–Jacobi map, Regulator, Deligne cohomology, Higher Chow group.
Publisher URL http://journals.cambridge.org/action/displayFulltext?type=1&fid=414274&jid=COM&volumeId=142&issueId=02&aid=414272

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