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arXiv · 2512.00568

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

Alejandro De Las Penas Castano
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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.

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Alejandro De Las Penas Castano. 2025-11-29. Zero cycles on products of elliptic curves over local fields with supersingular reduction. https://arxiv.org/abs/2512.00568

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