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Bloch’s conjecture, Deligne cohomology and higher Chow groups

By Morihiko Saito


We express the kernel of Griffiths ’ Abel-Jacobi map by using the inductive limit of Deligne cohomology in the generalized sense (i.e. absolute Hodge cohomology of A. Beilinson). This generalizes a result of L. Barbieri-Viale and V. Srinivas in the surface case. We prove a special case of Nori’s conjecture on Griffiths group, and generalize a formula for the Abel-Jacobi map of higher cycles due to Beilinson and Levine to the smooth non proper case. We also give a sufficient condition for the transcendental part of the image by the Abel-Jacobi map of a higher cycle on an elliptic surface to be nontrivial, and construct some examples

Year: 2002
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