The Abel-Jacobi map for higher Chow groups. II

DOI10.1007/s00222-007-0066-xzbMath1139.14010arXivmath/0611333OpenAlexW2761640084WikidataQ57445980 ScholiaQ57445980MaRDI QIDQ2458879

James D. Lewis, Matthew Kerr

Publication date: 5 November 2007

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611333

zbMATH Keywords

Abel-Jacobi maphigher Chow groupregulator mapabsolute Hodge cohomology

Mathematics Subject Classification ID

Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (22)

Algebraic and Arithmetic Properties of Period Maps ⋮ Normal functions, Picard-Fuchs equations, and elliptic fibrations on \(K3\) surfaces ⋮ Limits and singularities of normal functions ⋮ Non-trivial elements in the Abel-Jacobi kernels of higher-dimensional varieties ⋮ The complexity of higher Chow groups ⋮ Regulator maps for higher Chow groups via current transforms ⋮ Apéry extensions ⋮ Integral Deligne cohomology for real varieties ⋮ Simplicial Abel-Jacobi maps and reciprocity laws ⋮ Néron models and limits of Abel–Jacobi mappings ⋮ Rationally inequivalent points on hypersurfaces in \(\mathbb{P}^n\) ⋮ Indecomposable cycles and arithmetic normal functions ⋮ An explicit basis for the rational higher Chow groups of abelian number fields ⋮ Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles ⋮ A commutative regulator map into Deligne-Beilinson cohomology ⋮ Integral regulators for higher Chow complexes ⋮ Beilinson's Hodge Conjecture for Smooth Varieties ⋮ A Feynman integral via higher normal functions ⋮ Lectures on Hodge theory and algebraic cycles ⋮ Motives of some Fano varieties ⋮ Arithmetic normal functions and filtrations on Chow groups ⋮ Two applications of the integral regulator

Cites Work

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• Hodge-type conjecture for higher Chow groups
• Théorie de Hodge. II. (Hodge theory. II)
• Higher normal functions and Griffiths groups
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• Exterior products of zero-cycles
• Higher Abel-Jacobi maps for 0-cycles
• A Survey of the Hodge Conjecture
• Cycle map for strictly decomposable cycles
• The Abel–Jacobi map for higher Chow groups
• Mixed Hodge modules

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