Ramified covers of abelian varieties over torsion fields

Lior Bary-Soroker; Arno Fehm; Sebastian Petersen

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arXiv · 2206.01582

Ramified covers of abelian varieties over torsion fields

Lior Bary-Soroker·Arno Fehm·Sebastian Petersen

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Abstract

We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of $\mathbb{Q}$. In particular, we prove that every elliptic curve $E$ over $\mathbb{Q}$ has the weak Hilbert property of Corvaja-Zannier both over the maximal abelian extension $\mathbb{Q}^{\rm ab}$ of $\mathbb{Q}$, and over the field $\mathbb{Q}(A_{\rm tor})$ obtained by adjoining to $\mathbb{Q}$ all torsion points of some abelian variety $A$ over $\mathbb{Q}$.

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Lior Bary-Soroker, Arno Fehm, Sebastian Petersen. 2022-06-03. Ramified covers of abelian varieties over torsion fields. https://arxiv.org/abs/2206.01582

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