The canonical height and elliptic surfaces
The canonical height and elliptic surfaces
复制标题
规范高度和椭圆面
DOI：
10.1016/0022-314x(90)90073-z
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发表时间：
1990
影响因子：
0.7
通讯作者：
Masato Kuwata
中科院分区：
文献类型：
--
作者：
Masato Kuwata
设π：S→P_1是复数上的椭圆曲面。设E是S的一般纤维，则E是亏格1的曲线，我们假设它在K=C(U)上有一个有理点。根据Mordell-Weil定理，我们知道E(K)是有限生成的。在本文中，作者使用正则高度对来帮助确定E(K)。特别地，假设E(K)的秩为r，那么作者感兴趣的是确定r个分段是否构成基。作为例证，作者研究了方程A4+B4=C4+D4
Abstract Let π: S→ P 1 be an elliptic surface over the complex numbers. Let E be the generic fiber of S. Then E is a curve of genus 1 which we assume has a rational point over K= C (u). By the Mordell-Weil theorem, one knows that E (K) is finitely generated. In this paper the author uses the canonical height pairing to help in determining E (K). In particular, suppose that the rank of E (K) is r. Then the author is interested in determining whether r sections form a basis. As an illustration, the author examines the equation A 4+ B 4= C 4+ D 4