A simple construction of indecomposable higher Chow cycles in elliptic surfaces

2014/02/01 by Masanori Asakura, Asakura, Masanori
Mathematics · #19E15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:19E15

paper · pdf · doi:10.48550/arxiv.1402.0074

9 pages

openalex publication_date 2014/02/01 · arxiv created 2014/02/12 · arxiv updated 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I construct regulator indecomposable higher Chow cycles in elliptic surfaces satisfying certain conditions. As an application I give an alternative proof of a theorem of Gordon and Lewis, which asserts that there is a real regulator indecomposable cycles in a product of general elliptic curves.

Related

• Indecomposable Higher Chow cycles on Jacobians
• Higher Chow cycles on Eisenstein K3 surfaces
• Real Regulator on K₁ of elliptic surfaces
• Construction of Higher Chow cycles on cyclic coverings of ℙ¹ × ℙ¹
• Indecomposable K₁ and the Hodge-D-conjecture for K3 and Abelian Surfaces