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arXiv · 2512.06970

On the Chow group of elliptic surfaces over number fields

Domenico Valloni
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Abstract

Let $X$ be a smooth projective surface over a number field $K$. Assume that $X$ has an elliptic fibration over $\mathbb{P}^1_K$ with at least one singular fibre and a section. Let $\mathcal{X}/U$ be a smooth projective model of $X$ over some open subset $U \subset \mathrm{Spec}(\mathcal{O}_K)$. We show that $\ker\bigl(\mathrm{CH}^2(\mathcal{X}) \rightarrow \mathrm{CH}^2(X)\bigr)$ is a finitely generated group.

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Domenico Valloni. 2025-12-07. On the Chow group of elliptic surfaces over number fields. https://arxiv.org/abs/2512.06970

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