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arXiv · 2605.07009

Weight of the De Rham-Betti Structures of Abelian Varieties

Zekun Ji
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Abstract

In this note, we prove that for any abelian variety defined over $\overline{\mathbb{Q}}$, its de Rham-Betti (dRB) group necessarily contains $\mathbb{G}_{m}$ as the group of homotheties. Consequently, this rules out the existence of non-zero dRB classes in odd-degree cohomology groups of abelian varieties over $\overline{\mathbb{Q}}$. This generalises results of the first part of arXiv:2511.01072.

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Zekun Ji. 2026-05-07. Weight of the De Rham-Betti Structures of Abelian Varieties. https://arxiv.org/abs/2605.07009

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