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The Abel–Jacobi map for higher Chow groups

Published online by Cambridge University Press:  13 March 2006

Matt Kerr
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USAmatkerr@math.uchicago.edu
James D. Lewis
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canadalewisjd@gpu.srv.ualberta.ca
Stefan Müller-Stach
Affiliation:
Fachbereich 08, Institut für Mathematik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germanymueller-stach@uni-mainz.de
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Abstract

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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.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2006