Constructing Indecomposable Motivic Cohomology Classes on Algebraic Surfaces

Abstract

We describe a method to construct indecomposable classes in Bloch's higher Chow group $C{H}^2(X,1)$ on algebraic surfaces over the complex numbers via transcendental methods and apply it to obtain examples on K3-surfaces and some surfaces of general type.

Latex 2e, 34 pages

Cited by in corpus (25)

• Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups
• Indecomposable K_1 and the Hodge-D-conjecture for K3 and Abelian Surfaces
• Cycle Map for Strictly Decomposable Cycles
• The transcendental part of the regulator map for K_1 on a mirror family of K3 surfaces
• On algebraic mixed Hodge substructures of H^2
• Hodge-type conjecture for higher Chow groups
• Higher Chow cycles on a family of Kummer surfaces
• Non-Archimedean regulator maps and special values of L-functions
• A non-Archimedean analogue of the Hodge-D-conjecture for products of elliptic curves
• Tangent spaces to motivic cohomology groups
• Differential equations associated to Families of Algebraic Cycles
• The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles
• Nonvanishing of External Products for Higher Chow Groups
• On Mildenhall's Theorem
• Indecomposable Higher Chow Cycles on Low Dimensional Jacobians
• Zero-cycles on self-product of modular curves
• Arithmetic Mixed Sheaves
• Noether-Lefschetz for K_1 of a Surface, Revisited
• On the Beilinson-Hodge conjecture for $H^2$ and rational varieties
• Beilinson's Hodge conjecture for smooth varieties
• First and second $K$-groups of an elliptic curve over a global field of positive characteristic
• Higher Chow cycles on some K3 surfaces with involution
• Unramified cohomology, integral coniveau filtration and Griffiths group
• Limits and Singularities of Normal Functions
• A simple construction of indecomposable higher Chow cycles in elliptic surfaces