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The Abel–Jacobi map for higher Chow groups

Published online by Cambridge University Press:  13 March 2006

Matt Kerr ,
James D. Lewis  and
Stefan Müller-Stach
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.

Keywords

Abel–Jacobi mapregulatorDeligne cohomologyhigher Chow group14C2514C3014C3519E15
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 2 , March 2006 , pp. 374 - 396
Copyright
Foundation Compositio Mathematica 2006