关于某些椭圆曲线的Tate-Shafarevich群的注记(英文)  

A Note on the Tate-Shafarevich Group of Some Elliptic Curves

作　　者：张绍伟[1] 

机构地区：[1]北京大学数学系

出　　处：《数学进展》1997年第6期551-555,共5页Advances in Mathematics（China）

摘　　要：本文首先考察某个四元代数．通过对此四元代数的算术的研究，得到某类丢番图方程的解数与某些虚二次域类数之间的关系．最后，应用Ｔｕｎｎｅｌ的定理，得到一簇椭圆曲线的Ｔａｔｅ－Ｓｈａｆａｒｅｖｉｃｈ群的阶的上界．In this paper, we firstly consider a quaternion algebra. By studying the arithmetic of the quaternion, we get a relation between the numbers of solutions of a family of Diophantine equations and the class numbers of some imaginary quadratic fields. Finally by using Tunnell's theorem we get an upper bound for the order of the Tate-Shafarevich groups of a family of elliptic curves.

关 键 词：四元代数 T-S群 椭圆曲线 丢番图方程 

分 类 号：O156.7[理学—数学]