A note on the ramification of torsion points lying on curves of genus at least two
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چکیده
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 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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تاریخ انتشار 2009