The Abel-Jacobi map for higher Chow groups

Matt Kerr; James D. Lewis; Stefan Müller-Stach

doi:10.1112/S0010437X05001867

The Abel-Jacobi map for higher Chow groups

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

Department of Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

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.

Original language	English
Pages (from-to)	374-396
Number of pages	23
Journal	Compositio Mathematica
Volume	142
Issue number	2
DOIs	https://doi.org/10.1112/S0010437X05001867
State	Published - 2006

Keywords

Abel-Jacobi map
Deligne cohomology
Higher chow group
Regulator

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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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AU - Lewis, James D.

AU - Müller-Stach, Stefan

PY - 2006

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AB - 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.

KW - Abel-Jacobi map

KW - Deligne cohomology

KW - Higher chow group

KW - Regulator

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DO - 10.1112/S0010437X05001867

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SP - 374

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JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 2

ER -

The Abel-Jacobi map for higher Chow groups

Abstract

Keywords

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