The Abel-Jacobi map for higher Chow groups
classification
🧮 math.AG
keywords
abel-jacobichowcomplexgroupshighervarietiesbeilinsonbloch
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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.
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