AN INFINITE FAMILY OF ELLIPTIC CURVES AND GALOIS MODULE STRUCTURE
AN INFINITE FAMILY OF ELLIPTIC CURVES AND GALOIS MODULE STRUCTURE
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椭圆曲线和伽罗瓦模块结构的无限族
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. Klebel
中科院分区：
文献类型：
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作者：
W. Bley;M. Klebel
设 E 是在数域 F 上定义的椭圆曲线，且处处都有良好的约简。泰勒通过将F有理挠点除以E·M·群律，定义了一定的Kummer阶并研究了它们的伽罗瓦模结构。他的结果导致了这样的猜想：这些 Kummer 阶数相对于明确给出的 Hopf 阶数是自由的。在本文中，我们证明该猜想对于无限多个在二次虚数域 k 上定义且具有 k 有理 2 扭点的椭圆曲线不成立。
Let E be an elliptic curve dened over a number eld F with everywhere good reduction. By dividing F -rational torsion points with respect to the group law of E M. Taylor dened certain Kummer orders and studied their Galois module structure. His results led to the conjecture that these Kummer orders are free over an explicitly given Hopf order. In this paper we prove that the conjecture does not hold for innitely many elliptic curves which are dened over quadratic imaginary number elds k and endowed with a k-rational 2torsion point.