The Abel-Jacobi Map for Higher Chow Groups, II
Kerr, Matt · Lewis, James D.
Original · EN
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.
English translation
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