, Volume 354, Issue 3, pp 1029-1047
Date: 13 Dec 2011

Period and index of genus one curves over global fields

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Abstract

The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over a given global field, as long as the characteristic of the field does not divide the period.