Corpus ID: 212725054

Cubic function fields with prescribed ramification

  title={Cubic function fields with prescribed ramification},
  author={Valentijn Karemaker and Sophie Marques and Jeroen Sijsling},
  journal={arXiv: Number Theory},
  • Valentijn Karemaker, Sophie Marques, Jeroen Sijsling
  • Published 2020
  • Mathematics
  • arXiv: Number Theory
  • This article describes cubic function fields $L/K$ with prescribed ramification, where $K$ is a rational function field. We give general equations for such extensions, an algorithm to obtain an explicit defining equation when the purely cubic closure $K'/K$ of $L/K$ has genus zero, and a description of the twists of $L/K$ up to isomorphism over $K$. For cubic function fields of genus at most one, we also describe the twists and isomorphism classes obtained when one allows Mobius transformations… CONTINUE READING