Zero cycles on products of elliptic curves over local fields with supersingular reduction

2025/11/29 by Alejandro De Las Penas Castano, Castano, Alejandro De Las Penas
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2512.00568

Abstract

For a product E₁× E₂ of two elliptic curves over a p-adic field with good supersingular reduction, we produce infinitely many rational equivalences in the Chow group CH₀(X) of zero cycles via genus 2 covers of E₁ and E₂. We use this to obtain evidence for a conjecture of Colliot-Thélène about the structure of the Albanese kernel.

Citations

• Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's conjecture for zero-cycles
• Torsion phenomena for zero-cycles on a product of curves over a number field
• Zero-cycles on a product of elliptic curves over a p-adic field
• A finer Tate duality theorem for local Galois symbols

Related

• Zero-cycles on a product of elliptic curves over a p-adic field
• On the cycle map for products of elliptic curves over a p-adic field
• Zero-cycles on quasi-projective surfaces over p-adic fields
• Divisibility Results for zero-cycles
• Global Galois Symbols on E x E