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The Abel-Jacobi map for higher Chow groups

Matt Kerr·James Lewis·Stefan Müller-Stach
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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.

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Matt Kerr, James Lewis, Stefan Müller-Stach. 2004-09-07. The Abel-Jacobi map for higher Chow groups. https://arxiv.org/abs/math/0409116

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