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Journal of the London Mathematical Society 2001 63(2):275-287; doi:10.1017/S0024610700001812
© 2001 by London Mathematical Society
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© The London Mathematical Society

Espaces Homogènes Principaux et Points de 2-Division de Courbes Elliptiques

Philippe Cassou-Noguès and Arnaud Jehanne

Laboratoire de Théorie des Nombres et d'Algorithmique Arithmétique, Université Bordeaux I Cours de la Libération, 33405 Talence Cedex, France

Received 8 October 1998. Revision received 23 June 1999.

Dans cet article, nous nous intéressons aux problèmes de structure galoisienne associés aux couples (E/L, a), E désigne une courbe elliptique définie sur le corps de nombres L et a un endomorphisme de E. Si E est à multiplication complexe, nous notons k le corps quadratique imaginaire dont l'anneau des entiers décrit End(E) et L une extension de k. Ainsi a est-il selon les cas un entier algébrique de k ou un élément de Z.


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