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The Abel–Jacobi map for higher Chow groups
James D. LewisMatt KerrStefan Müller-stachsubject
AlgebraDeligne cohomologyPure mathematicsMathematics::Algebraic GeometryAlgebra and Number TheoryMathematics::K-Theory and HomologyHomology (mathematics)Chow ringMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-03-01 | Compositio Mathematica |