An elliptic curve defined over a number field possesses only a finite number of torsion points defined over the cyclotomic closure of its field of definition. In analogy to the relative version of the Manin–Mumford conjecture stated by Masser and Zannier, we propose a family version of the above statement and prove it under a suitable integrality condition.

中文翻译：

---

椭圆方案中的旋回扭点

在数域上定义的椭圆曲线仅具有在其定义域的分圆闭合上定义的有限数量的扭转点。类比于 Masser 和 Zannier 提出的 Manin-Mumford 猜想的相对版本，我们提出了上述陈述的家庭版本，并在合适的完整性条件下证明了它。