Geodesic
Number Theory
Torsion anomalous points and families of elliptic curves
[Points de torsion et familles de courbes elliptiques]

Présenté par : Jean-Pierre Serre

Masser, David1 ; Zannier, Umberto2
1 Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
2 Scuola Normale, Piazza Cavalieri 7, 56126 Pisa, Italy
Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 491-494.

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We prove that there are at most finitely many complex λ≠0,1 such that two points on the Legendre elliptic curve Y2=X(X−1)(X−λ) with coordinates X=2 and X=3 both have finite order. This is a very special case of some well-known conjectures on unlikely intersections with varying semiabelian varieties.

Comme cas très spécial de certaines conjectures générales sur l'intersection d'une variété algébrique avec la réunion des sous-schémas de dimension fixée d'un schéma semi-abélien, nous montrons qu'il n'existe qu'un nombre fini de λ∈C∖{0,1} tels que les quatre points de la courbe elliptique Y2=X(X−1)(X−λ) avec X=2 et X=3 soient d'ordre fini.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2008.03.024

Masser, David 1 ; Zannier, Umberto 2

1 Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
2 Scuola Normale, Piazza Cavalieri 7, 56126 Pisa, Italy 
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Masser, David; Zannier, Umberto. Torsion anomalous points and families of elliptic curves. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 491-494. doi : 10.1016/j.crma.2008.03.024. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2008.03.024/

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