论文标题
关于在阿贝里亚品种的分支封面上的理性点的分布
On the distribution of rational points on ramified covers of abelian varieties
论文作者
论文摘要
我们证明了有关在有限生成的特征零的$ k $ abelian品种覆盖范围上的理性点分布的新结果。例如，鉴于$ a $的$ a $在$ k $上是一个$ k $的$ a $，带有$ k $ - 合理点的$ a $，我们证明有有限的inite-index coset $ c \ subset a（k）$，因此$π（x（k））$是$ c $的，因此我们证明有有限的inite inite inite inite intex coset $ c \ subset a（k）$。 目前，我们的结果似乎没有其他可用的其他方法。他们证实了Lang对理性点的猜想的预测，并且也朝着Serre提出的有关逆Galois问题的应用方向的方向。最后，我们作品的结论可能被视为希尔伯特（Hilbert）不可约性定理的敏锐版本。
We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields $k$ of characteristic zero. For example, given a ramified cover $π: X \to A$, where $A$ is an abelian variety over $k$ with a dense set of $k$-rational points, we prove that there is a finite-index coset $C \subset A(k)$ such that $π(X(k))$ is disjoint from $C$. Our results do not seem to be in the range of other methods available at present; they confirm predictions coming from Lang's conjectures on rational points, and also go in the direction of an issue raised by Serre regarding possible applications to the Inverse Galois Problem. Finally, the conclusions of our work may be seen as a sharp version of Hilbert's irreducibility theorem for abelian varieties.
