Abstract: | Let k be an algebraic number field of degree n on 2; and , respectively, the curves on k; let, and m, 'm be the bases of groups of all points of order m on and g, respectively. A proof of the following theorem is sketched: let p>3 be prime; if, then (pt)6n; if k, then (pt)4n. The resulting bounds are unimprovable.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 57–65, 1986. |