The Abel–Jacobi map for higher Chow groups, II
By M. Kerr, J. Lewis. Compositio Mathematica, 2004
115 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1d7671fc9cbf4e7710cff5613a6c550d4c2136c0
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In Geometry and Topology
- Pierre Vanhove
- M. Kerr
- Spencer Bloch
- Charles F. Doran
- L. Tancredi
- Ettore Remiddi
- Alexander V. Kitaev
- Claude Duhr
In Mathematical Physics
- Pierre Vanhove
- M. Kerr
- Charles F. Doran
- Spencer Bloch
- L. Tancredi
- Ettore Remiddi
- Minhyong Kim
- Claude Duhr
Citations in the corpus
- Algebraic K-theory of toric hypersurfaces (2008, background): “The KLM currents (Z → TZ,ΩZ, RZ) give a map of complexes (described in full in [49]) inducing an Abel–Jacobi map from H2n+∗ M (Y,Q(n)) to H2n+∗ D (Y,Q(n)) ∗<0 ∼= Ext MHS (Q(0), H2n+∗−1(Y,Q(n))) ∗≤−n ∼= H2n+∗−1(Y,C/Q(n)).”
- The elliptic dilogarithm for the sunset graph (2013, methodology): “The technology of currents as developed by Kerr and collaborators in [38] provides an alternate approach to the motivic calculations.”