Number theory
The truth about torsion in the CM case
[La vérité sur la torsion dans le cas CM]

Présenté par : Jean-Pierre Serre

Clark, Pete L.1 ; Pollack, Paul1
1 Department of Mathematics, University of Georgia, Athens, GA, 30602, USA
Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 683-688.

Soit TCM(d) la taille maximale du sous-groupe de torsion d'une courbe elliptique à multiplications complexes, définie sur un corps de nombres de degré d. Nous montrons qu'il existe C une constante absolue, effective, telle que TCM(d)≤Cdlog⁡log⁡(d) pour tout d≥3.

Let TCM(d) be the maximum size of the torsion subgroup of an elliptic curve with complex multiplication over a degree d number field. We show there is an absolute, effective constant C such that TCM(d)≤Cdlog⁡log⁡d for all d≥3.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.05.004
Clark, Pete L. 1 ; Pollack, Paul 1

1 Department of Mathematics, University of Georgia, Athens, GA, 30602, USA 
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Clark, Pete L.; Pollack, Paul. The truth about torsion in the CM case. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 683-688. doi : 10.1016/j.crma.2015.05.004. http://archive.numdam.org/articles/10.1016/j.crma.2015.05.004/

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