Torsion phenomena for zero-cycles on a product of curves over a number field

2022/04/12 by Gazaki, Evangelia, Love, Jonathan · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.05876

Abstract

For a smooth projective variety X over a number field k a conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map of X is a torsion group. In this article we consider a product X=C₁×⋯× C_d of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true for X. Additionally, we produce many new examples of non-isogenous elliptic curves E₁, E₂ with positive rank over ℚ for which the image of the natural map E₁(ℚ)⊗ E₂(ℚ)\xrightarrowε CH₀(E₁× E₂) is finite, including the first known examples of rank greater than 1. Combining the two results, we obtain infinitely many nontrivial products X=C₁×⋯× C_d for which the analogous map ε has finite image.

Cited by

• Zero cycles on products of elliptic curves over local fields with supersingular reduction
• Density of algebraic points on products of curves

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