论文标题
在椭圆曲线的横向曲线上的$ K $合理点的显式高度界限
Explicit height bounds for $K$-rational points on transverse curves in powers of elliptic curves
论文作者
论文摘要
令$ c $为椭圆曲线$ e $的功率$ e^n $的代数曲线。在本文中，我们对所有适当的代数子群的$ e^n $的$ c $上的所有代数点的高度产生了良好的明确约束。该方法在椭圆情况下给出了Manin-dam'janenko定理的完全明确的版本，并且仅当$ e $没有复杂的乘法时，这是对先前结果的概括。
Let $C$ be an algebraic curve embedded transversally in a power $E^N$ of an elliptic curve $E$. In this article we produce a good explicit bound for the height of all the algebraic points on $C$ contained in the union of all proper algebraic subgroups of $E^N$. The method gives a totally explicit version of the Manin-Dam'janenko Theorem in the elliptic case and it is a generalisation of previous results only proved when $E$ does not have Complex Multiplication.
