ON THE p-TORSION OF ELLIPTIC CURVES AND ELLIPTIC SURFACES IN CHARACTERISTIC p
نویسنده
چکیده
We study the extension generated by the x-coordinates of the petorsion points of an elliptic curve over a function field of characteristic p. If S → C is a non-isotrivial elliptic surface in characteristic p with a pe-torsion section, then for pe > 11 our results imply restrictions on the genus, the gonality, and the p-rank of the base curve C, whereas for pe ≤ 11 such a surface can be constructed over any base curve C. We also describe explicitly all occurring pe in the cases where the surface S is rational or K3 or the base curve C is rational, elliptic or hyperelliptic.
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تاریخ انتشار 2004