## A note on the ramification of torsion points lying on curves of genus at least two.(English)Zbl 1223.11075

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 $$p$$ 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. The author shows that the coordinates of the torsion points of Jac($$C$$) lying on $$C$$ are contained in the unique tamely ramified quadratic extension of the field generated over $$K$$ by the coordinates of the $$p$$-torsion points of Jac($$C)$$.

### MSC:

 11G20 Curves over finite and local fields 14H25 Arithmetic ground fields for curves 14H40 Jacobians, Prym varieties

### Keywords:

curves of genus at least two; jacobian; torsion points
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### References:

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