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

Alejandro De Las Penas Castano

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

Algebraic Geometry 2025-12-02 v1

Authors: Alejandro De Las Penas Castano

Abstract

For a product $E_1\times E_2$ of two elliptic curves over a $p$ -adic field with good supersingular reduction, we produce infinitely many rational equivalences in the Chow group $\mathrm{CH}_0(X)$ of zero cycles via genus 2 covers of $E_1$ and $E_2$ . We use this to obtain evidence for a conjecture of Colliot-Th\'el\`ene about the structure of the Albanese kernel.

Keywords

elliptic curves Chow group zero cycles rational equivalence genus 2 covers Albanese kernel Colliot-Th\'el\`ene conjecture supersingular reduction

Cite

@article{arxiv.2512.00568,
  title  = {Zero cycles on products of elliptic curves over local fields with supersingular reduction},
  author = {Alejandro De Las Penas Castano},
  journal= {arXiv preprint arXiv:2512.00568},
  year   = {2025}
}

Comments

21 pages, for SAGE code see https://alejandrodlpc.github.io/

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