The Abel-Jacobi Map for Higher Chow Groups, II
Matt Kerr, James D. Lewis
Abstract
We explicitly describe cycle-class maps cH 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 cH; this leads to new results on nontrivial indecomposable higher Chow cycles in the regulator kernel.
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