The Abel-Jacobi map for higher Chow groups

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1567625
• Publisher URL: http://journals.cambridge.org/action/displayFulltext?type=1&fid=414274&jid=COM&volumeId=142&issueId=02&aid=414272