Mathematische Annalen

, Volume 354, Issue 3, pp 1029–1047

Period and index of genus one curves over global fields

Article

DOI: 10.1007/s00208-011-0745-1

Cite this article as:
Sharif, S. Math. Ann. (2012) 354: 1029. doi:10.1007/s00208-011-0745-1
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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.

Mathematics Subject Classification (2000)

11G05

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.California State University San MarcosSan MarcosUSA