複乘數橢圓曲線的庫默擴張; Kummer Extensions on Elliptic Curves with Complex Multiplication

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/47063

Title:	複乘數橢圓曲線的庫默擴張;Kummer Extensions on Elliptic Curves with Complex Multiplication
Authors:	陳燕美
Contributors:	數學系
Keywords:	橢圓曲線;複乘數;二次體;伽羅瓦擴張;elliptic curves;complex multiplication;quadratic fields;Galois extensions;數學類
Date:	2010-08-01
Issue Date:	2011-07-13 16:25:19 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	令E 為定義在有理數上的一條橢圓曲線。假設E 有二次體中整數環的複乘數而且E 在質數q 為超奇異化歸。令P 為橢圓曲線E 上的有理點而且其階為無窮。令L 是K 加進所有q-扭轉點及所有Q 滿足[q]Q=P 的座標的擴張體。本計畫希望深入探討這個伽羅瓦擴張。 Let E be an elliptic curve defined over the rational numbers. Suppose that E has complex multiplication by a maximal order of an imaginary quadratic field K and has good supersingular reduction at a prime q. Let P be a rational point on E of infinite order. Denote by L the extension field joining the coordinates of q-torsion points of E and also the coordinates of all points Q satisfying [q]Q=P. In this project, we study the Galois extension L over K. 研究期間：9908 ~ 10007
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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