CM liftings of supersingular elliptic curves

نویسنده

  • BEN KANE
چکیده

Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by OD to supersingular elliptic curves in characteristic p. In the algorithm we first determine an explicit constant Dp so that |D| > Dp implies that the map is necessarily surjective and then we compute explicitly the cases |D| < Dp. Supposant vraie la conjecture de Riemann généralisée nous présentons un algorithme qui, donné un nombre prémier p, calcule l’ensemble des discriminants fondamentaux D < 0 tels que l’application de reduction modulo un premier aux dessus p des courbes elliptiques avec multiplication complexe par OD vers les courbes elliptiques supersingular en characteristique p est surjective. Dans l’algorithme, nous d’abord determinons une borne Dp explicite, tel que |D| > Dp implique que l’application est necessairement surjective et puis nous calculons explicitement les cas |D| < Dp.

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تاریخ انتشار 2009