Period and index of genus one curves over global fields
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- Sharif, S. Math. Ann. (2012) 354: 1029. doi:10.1007/s00208-011-0745-1
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.