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Modèles minimaux des espaces principaux homogènes sur les courbes elliptiques

In: Proceedings of a Conference on Local Fields

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  • A. Néron

Abstract

Résumé Le théorème d’existence d’un modèle 𝔭-simple 𝔭-minimal pour une courbe elliptique n’est démontré dans [6], chap. III que dans le cas où cette courbe possède un point rationnel sur le corps de base (local ou global) k, c’est-à-dire dans le cas où l’on peut munir cette courbe d’une structure de variété abélienne A, définie sur k. Je me propose d’exposer ici, tout au moins dans ses grandes lignes, une démonstration d’un théorème d’existence analogue, valable pour une courbe elliptique quelconque définie sur k, mais ne possèdant pas nécessairement un point rationnel sur k — ou, si l’on préfère, valable pour un espace principal homogène sur A, défini sur k.

Suggested Citation

  • A. Néron, 1967. "Modèles minimaux des espaces principaux homogènes sur les courbes elliptiques," Springer Books, in: T. A. Springer (ed.), Proceedings of a Conference on Local Fields, pages 66-77, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-87942-5_7
    DOI: 10.1007/978-3-642-87942-5_7
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