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Some remarks concerning points of finite order on elliptic curves over global fields. (English) Zbl 0348.14018

MSC:
14H25 Arithmetic ground fields for curves
14H45 Special algebraic curves and curves of low genus
14G05 Rational points
14G20 Local ground fields in algebraic geometry
14G25 Global ground fields in algebraic geometry
11R58 Arithmetic theory of algebraic function fields
11D99 Diophantine equations
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[1] Demjanenko, V. A., Points of finite order on elliptic curves (Russian).Acta Arith., (1971), 185–194.
[2] Frey, G., Elliptische Funktionenkörper mit schlechter Reduktion und nichttrivialer Hasse-Invariante.Archiv d. Math.,XXIII, (1972), 260–268. · Zbl 0238.14013
[3] Frey, G., Elliptische Kurven über bewerteten Körpern;Manuskript.
[4] Hellegouarche, J., Points d’ordre 2ph sur les courbes elliptiques.Acta Arith.,26 (1975), 253–263.
[5] Igusa, J., Kroneckerian model of fields of elliptic modular functions.Amer. J. Math.,81 (1959), 561–577. · Zbl 0093.04502
[6] Lutz, E., Sur l’équationY 2=X 3X dans les corpsp-adiques.J. reine angew. Math. 177 (1937), 238–244. · Zbl 0017.05307
[7] Neron, A., Modèles minimaux des variétés abéliennes sur les corps locaux et globaux.Publ. Math. IHES 21 (1974).
[8] Olson, L. D., Points of finite order on elliptic curves with complex multiplication.Manus. Math.,14 (1974), 195–205. · Zbl 0292.14015
[9] Olson, L. D., Torsion points on elliptic curves with givenj-invariant.Manus. Math.,16 (1975), 145–150. · Zbl 0314.14006
[10] Samuel, P., Compléments à un article de Hans Grauert sur la conjecture de Mordell.Publ. Math. IHES 29 (1966), 55–62. · Zbl 0144.20102
[11] Serre, J. P., Propriétés galoisiennes des points d’ordre fini des courbes elliptiques.Invent. math. 15 (1972), 259–331. · Zbl 0235.14012
[12] Roquette, P., Analytic theory of elliptic functions over local fields.Hamb. Math. Einzelschriften, Neue Folge, Heft 1 (1969). · Zbl 0169.38001
[13] Zimmer, H. G., Points of finite order on elliptic curves over number fields.To appear in Archiv d. Math. · Zbl 0349.14014
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