The Abel-Jacobi Map for Higher Chow Groups, II

Details The Abel-Jacobi Map for Higher Chow Groups, II The Abel-Jacobi Map for Higher Chow Groups, II

2006-11-11

arxiv.org/abs/math/0611333v1

Mathematics

Algebraic Geometry

68 pages, 3 figures

Scientific paper

10.1007/s00222-007-0066-x

We explicitly describe cycle-class maps c_H from motivic cohomology to absolute Hodge cohomology, for smooth quasi-projective and (some) proper singular varieties, and compute special cases of the latter. For smooth projective varieties, we also study Hodge-theoretically defined "higher Abel-Jacobi maps" on the kernel of c_H; this leads to new results on nontrivial indecomposable higher Chow cycles in the regulator kernel.

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