An infinite family of elliptic curves over Q with large rank via Néron's method
An infinite family of elliptic curves over Q with large rank via Néron's method
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通过 Néron 方法得出 Q 上具有大秩的无限族椭圆曲线
DOI：
10.1007/bf01243907
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发表时间：
1991
影响因子：
3.1
通讯作者：
T. Shioda
中科院分区：
文献类型：
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作者：
T. Shioda
N6 ron在他的著名文章[N1]中给出了构造Q上秩至少为11的无限族椭圆曲线的方法。从Mordell-Weil格[IS 1，S 2，S 3]的角度研究这一问题，发现N6 ron方法给出了构造这一格的一个完整算法.特别地，我们可以写出一个明确的数值例子。N6 ron的想法是代数几何和数论中一些深刻结果的一个非常巧妙、美丽的结合。前者基于del Pezzo曲面理论（参见。[M，DP]），后者是起源于N6 ron的专业化论点，这一论点得到了Silverman和Tate的加强（参见。[Sil，T]）。另一个隐含在[N1]中的成分似乎是导致函数域上椭圆曲线的Kodaira-N6 ron模型（椭圆曲面）的想法，该模型后来在[N2]中得到发展。我们的贡献，如果有的话，将是：
In his famous article [N1], N6ron has given a method for constructing an infinite family of elliptic curves over Q with rank at least 11. By studying this from the viewpoint of Mordell-Weil lattices IS 1, S 2, S 3], we find that N6ron's method gives a complete algorithm for such a construction. In particular, we can write down an explicit numerical example. N6ron's idea is a very ingeneous, beautiful combination of some deep results in algebraic geometry and number theory. The former is based on the theory of del Pezzo surfaces (cf. [M, DP]) and the latter is the specialization argument originated by N6ron, which has been strengthened by Silverman and Tate (cf. [Sil , T]). Another ingredient implicit in IN1] seems to be the idea leading to the Kodaira-N6ron model (an elliptic surface) of an elliptic curve over a function field, which was to be developed later in [N2]. Our contribution, if any, will be:
Tetsuji Shioda：“通过 Weyl 群的不变量构建高阶椭圆曲线”
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