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

Damian Rössler — 2010

Journal de Théorie des Nombres de Bordeaux

Let C be a curve of genus g 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 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...

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