The Abel-Jacobi Map for Higher Chow Groups, II

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

References in corpus (3)

• The Leray spectral sequence is motivic
• Direct image of logarithmic complexes and infinitesimal invariants of cycles
• Hodge-type conjecture for higher Chow groups

Cited by in corpus (19)

• A Feynman integral via higher normal functions
• Arakelov motivic cohomology I
• An Exponential History of Functions with Logarithmic Growth
• Integral Regulators for Higher Chow Complexes
• Two applications of the integral regulator
• A commutative regulator map into Deligne-Beilinson cohomology
• Specialization of cycles and the K-theory elevator
• Apéry extensions
• Beilinson's Hodge Conjecture for K_1 revisited
• Weil-étale cohomology and zeta-values of arithmetic schemes at negative integers
• An explicit basis for the rational higher Chow groups of abelian number fields
• Integral Deligne Cohomology for Real Varieties
• Limits and Singularities of Normal Functions
• Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles
• The Business of Height Pairings
• Beilinson's Hodge conjecture for smooth varieties
• Simplicial Abel-Jacobi maps and reciprocity laws
• Abel-Jacobi isomorphism for one cycles on Kirwan's resolution of the moduli space SU_C(2,O_C)
• Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles