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arXiv · 2108.12405

Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties

Fabrizio Barroero·Lars Kühne·Harry Schmidt
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Abstract

Let $G$ be a semiabelian variety and $C$ a curve in $G$ that is not contained in a proper algebraic subgroup of $G$. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of $C$ with subgroups of codimension at least $2$. In this note, we establish this assertion for general semiabelian varieties over $\bar{\mathbb{Q}}$. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.

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Fabrizio Barroero, Lars Kühne, Harry Schmidt. 2021-08-27. Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties. https://arxiv.org/abs/2108.12405

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