THE p-TORSION SUBGROUP SCHEME OF AN ELLIPTIC CURVE
نویسنده
چکیده
Let k be a field of positive characteristic p. Question: Does every twisted form of μp over k occur as subgroup scheme of an elliptic curve over k? We show that this is true for most finite fields, for local fields and for fields of characteristic p ≤ 11. However, it is false in general for fields of characteristic p ≥ 13, which is related to the fact that the Igusa curves are not rational in these characteristics. Moreover, we also analyse twisted forms of p-torsion subgroup schemes of ordinary elliptic curves and the analogous problems for supersingular curves.
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