A note on the ramification of torsion points lying on curves of genus at least two

@article{Rössler2010,
abstract = {Let $C$ be a curve of genus $g\ge 2$ defined over the fraction field $K$ of a complete discrete valuation ring $R$ with algebraically closed residue field. Suppose that $\operatorname\{char\}(K)=0$ and that the characteristic $p$ of the residue field is not $2$. Suppose that the Jacobian $\operatorname\{Jac\}(C)$ has semi-stable reduction over $R$. Embed $C$ in $\operatorname\{Jac\}(C)$ 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 $\operatorname\{Jac\}(C)$.},
affiliation = {Département de Mathématiques Bâtiment 425 Faculté des Sciences d’Orsay Université Paris-Sud 91405 Orsay Cedex, FRANCE},
author = {Rössler, Damian},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {curves of genus at least two; jacobian; torsion points},
language = {eng},
number = {2},
pages = {475-481},
publisher = {Université Bordeaux 1},
title = {A note on the ramification of torsion points lying on curves of genus at least two},
url = {http://eudml.org/doc/116415},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Rössler, Damian
TI - A note on the ramification of torsion points lying on curves of genus at least two
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 2
SP - 475
EP - 481
AB - Let $C$ be a curve of genus $g\ge 2$ defined over the fraction field $K$ of a complete discrete valuation ring $R$ with algebraically closed residue field. Suppose that $\operatorname{char}(K)=0$ and that the characteristic $p$ of the residue field is not $2$. Suppose that the Jacobian $\operatorname{Jac}(C)$ has semi-stable reduction over $R$. Embed $C$ in $\operatorname{Jac}(C)$ 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 $\operatorname{Jac}(C)$.
LA - eng
KW - curves of genus at least two; jacobian; torsion points
UR - http://eudml.org/doc/116415
ER -