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

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).

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).

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DOI : https://doi.org/10.5802/jtnb.727
@article{JTNB_2010__22_2_475_0,
     author = {Damian R\"ossler},
     title = {A note on the ramification of torsion points lying on curves of genus at least two},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {475--481},
     publisher = {Universit\'e Bordeaux 1},
     volume = {22},
     number = {2},
     year = {2010},
     doi = {10.5802/jtnb.727},
     mrnumber = {2769074},
     zbl = {1223.11075},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.727/}
}
Damian Rössler. A note on the ramification of torsion points lying on curves of genus at least two. Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 2, pp. 475-481. doi : 10.5802/jtnb.727. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.727/

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