A note on the ramification of torsion points lying on curves of genus at least two
Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 475-481.

Let C be a curve of genus g2 defined over the fraction field K of a complete discrete valuation ring R with algebraically closed residue field. Suppose that char(K)=0 and that the characteristic p of the residue field is not 2. Suppose that the Jacobian Jac(C) has semi-stable reduction over R. Embed C in Jac(C) using a K-rational point. We show that the coordinates of the torsion points lying on C lie in the unique tamely ramified quadratic extension of the field generated over K by the coordinates of the p-torsion points on Jac(C).

Soit C une courbe de genre g2 définie sur le corps de fractions K d’un anneau de valuation discret R dont le corps résiduel est algébriquement clos. On suppose que char(K)=0 et que la caractéristique résiduelle p de R n’est pas 2. On suppose aussi que la jacobienne Jac(C) de C a réduction semi-stable sur R. On plonge C dans Jac(C) via a un point K-rationnel. Nous montrons que les coordonnées des points de torsion de Jac(C) qui se trouvent dans C(K ¯) sont dans l’unique extension modérément ramifiée du corps engendré par les coordonnées des points de p-torsion de Jac(C).

DOI: 10.5802/jtnb.727
Rössler, Damian 1

1 Département de Mathématiques Bâtiment 425 Faculté des Sciences d’Orsay Université Paris-Sud 91405 Orsay Cedex, FRANCE
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Rössler, Damian. A note on the ramification of torsion points lying on curves of genus at least two. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 475-481. doi : 10.5802/jtnb.727. http://www.numdam.org/articles/10.5802/jtnb.727/

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