1999/08/05 by Masanori Asakura, Asakura, Masanori
Mathematics · #14C30 #32S35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14C30 #msc:32S35
paper · pdf · doi:10.48550/arxiv.math/9908019
Latex2e, 20pages
arxiv created 1999/08/05 · openalex publication_date 1999/08/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford invariant vanishes, but not higher Abel-Jacobi invariant.