تقرير
Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties
| العنوان: | Unlikely Intersections of Curves with Algebraic Subgroups in Semiabelian Varieties |
|---|---|
| المؤلفون: | Barroero, Fabrizio, Kühne, Lars, Schmidt, Harry |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, Primary 11G10, Secondary 03C64, 11G50, 14G40, 14K99 |
| الوصف: | 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. Comment: Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.12405 |
| رقم الأكسشن: | edsarx.2108.12405 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |