论文标题
较高属曲线上的可解决点
Solvable points on higher genus curves
论文作者
论文摘要
众所周知，对于在$ \ mathbb {q} $上定义的曲线，$ g \ leq 4 $的曲线，在$ \ mathbb {q} $的可溶解扩展上定义的曲线上存在一个点。我们将可溶剂扩展的属性曲线上的点与Bombieri-lang猜想相关联。具体而言，它表明，用固定的可溶解GALOIS组在扩展上定义的品种参数化点是一般类型的。此外，我们在这些品种中表明了某些亚变量的存在，暗示着曲线可解决的形态。
It is known that for a curve defined over $\mathbb{Q}$ of genus $g \leq 4$, there exists a point on the curve defined over a solvable extension of $\mathbb{Q}$. We relate points on curves of genus $g \geq 5$ over solvable extensions to the Bombieri-Lang conjecture. Specifically, it shows that varieties parameterising points defined over extensions with a fixed solvable Galois group are of general type. Moreover, we show the existence of certain subvarieties in these varieties imply the existence of solvable morphisms from the curve.
