On rational torsion points of central $\mathbb{Q}$-curves

Fumio Sairaiji; Takuya Yamauchi

doi:10.5802/jtnb.637

On rational torsion points of central

ℚ

-curves

Fumio Sairaiji ¹ ; Takuya Yamauchi ²

¹ Hiroshima International University, Hiro, Hiroshima 737-0112, Japan
² Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 465-483.

Abstract (VO)
Résumé

Let $E$ be a central $ℚ$ -curve over a polyquadratic field $k$ . In this article we give an upper bound for prime divisors of the order of the $k$ -rational torsion subgroup $E_{t o r s} (k)$ (see Theorems 1.1 and 1.2). The notion of central $ℚ$ -curves is a generalization of that of elliptic curves over $ℚ$ . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].

Soit $E$ une $ℚ$ -courbe centrale sur un corps polyquadratique $k$ . Dans cet article, nous donnons une borne supérieure des diviseurs premiers de l’ordre du sous-groupe de torsion $k$ -rationnel $E_{t o r s} (k)$ (voir Théorèmes 1.1 et 1.2). La notion de $ℚ$ -courbe centrale est une généralisation de celle de courbe elliptique sur $ℚ$ . Notre résultat est une généralisation du Théorème de Mazur [12], et c’est une précision des bornes supérieures de Merel [15] et Oesterlé [17].

MR Zbl

DOI : 10.5802/jtnb.637

Affiliations des auteurs :

Fumio Sairaiji ¹ ; Takuya Yamauchi ²

¹ Hiroshima International University, Hiro, Hiroshima 737-0112, Japan
² Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

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     title = {On rational torsion points of central $\mathbb{Q}$-curves},
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     publisher = {Universit\'e Bordeaux 1},
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Fumio Sairaiji; Takuya Yamauchi. On rational torsion points of central $\mathbb{Q}$-curves. Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 465-483. doi : 10.5802/jtnb.637. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.637/

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