论文标题
家庭曲线的理性点数的界限
Bounds on the number of rational points of curves in families
论文作者
论文摘要
在本说明中，我们给出了固定数字字段上平滑射击曲线积分点数的统一界数的替代证明，并在固定数量之外进行了良好的降低。我们使用的是，由于Bertin-Romagny，由Lawrence-Venkatesh建造的Kodaira-Parshin家族本身可以组装成一个家庭。然后，我们重复Lawrence-Venkatesh对P-ADIC时期图的研究，以及附近纤维的比较。
In this note, we give an alternative proof of uniform boundedness of the number of integral points of smooth projective curves over a fixed number field with good reduction outside of a fixed set of primes. We use that due to Bertin-Romagny, the Kodaira-Parshin families constructed by Lawrence-Venkatesh can themselves be assembled into a family. We then repeat Lawrence-Venkatesh's study of the p-adic period map, together with the comparison of nearby fibres.
