Period and index of genus one curves over global fields
- First Online:
- Cite this article as:
- Sharif, S. Math. Ann. (2012) 354: 1029. doi:10.1007/s00208-011-0745-1
- 125 Downloads
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.