Higher Abel-Jacobi maps for 0-cycles

2005/04/05 by Matt Kerr, Kerr, Matt
Mathematics · #14C25 #14C30 #14C35 #19D45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:14C25 #msc:14C30 #msc:14C35 #msc:19D45

paper · pdf · doi:10.48550/arxiv.math/0504086

58 pages, 1 figure; new section 16

openalex publication_date 2005/04/05 · arxiv created 2006/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting from the candidate Bloch-Beilinson filtration on Chow groups of 0-cycles constructed by J. Lewis, we develop and describe geometrically a series of Hodge-theoretic invariants defined on the graded pieces. Explicit formulas (in terms of currents and membrane integrals) are given for certain quotients of the invariants, with applications to 0-cycles on products of curves.

Related

• Arithmetic Hodge structure and higher Abel-Jacobi maps
• Higher Abel-Jacobi Maps
• A filtration on the higher Chow group of zero cycles on an abelian variety
• Filtrations of the Chow group of zero-cycles on abelian varieties and behavior under isogeny
• Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups