The Abel-Jacobi Map for Higher Chow Groups, II
arXiv:math/0611333 · doi:10.1007/s00222-007-0066-x
Abstract
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.
68 pages, 3 figures