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

2009/02/24 by Damian Rossler, Rossler, Damian
Mathematics · #14G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14G20

paper · pdf · doi:10.48550/arxiv.0902.4161

arxiv created 2009/02/24 · arxiv updated 2009/12/01

Abstract

Let C be a curve of genus g\geqslant 2 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 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 moderately ramified quadratic extension of the field generated over K by the coordinates of the p-torsion points on \Jac(C).

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