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Points rationnels sur les quotients d’Atkin-Lehner de courbes de Shimura de discriminant $p q$

Florence Gillibert — 2013

Annales de l’institut Fourier

Soient $p$ et $q$ deux nombres premiers distincts et $X^{p q} / w_{q}$ le quotient de la courbe de Shimura de discriminant $p q$ par l’involution d’Atkin-Lehner $w_{q}$ . Nous décrivons un moyen permettant de vérifier un critère de Parent et Yafaev en grande généralité pour prouver que si $p$ et $q$ satisfont des conditions de congruence explicites, connues comme les conditions du cas non ramifié de Ogg, et si $p$ est assez grand par rapport à $q$ , alors le quotient $X^{p q} / w_{q}$ n’a pas de point rationnel non spécial.

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