Abelian varieties having very bad reduction
نویسنده
چکیده
Let E be an elliptic curve over a field K with a discrete valuation v with residue class field k. Suppose E has "very bad reduction" at v, i.e. the connected component An of the special fibre An of the Neron minimal model is isomorphic to ffi . Then U cl the order of An(k)/A„(k) is at most 4 äs can be seen by inspection of the usual tables, cf.[9], pp. 124/125, cf. [5], p.46. Thus it follows that if the order of the torsion subgroup Tors(E(K)) is at least 5 and prime to p = char(k), the reduction cannot be very bad. This note arose from an attempt to see whether an explicit classification really is necessary to achieve this result.
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تاریخ انتشار 2005