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Cubic Function Fields with Prescribed Ramification by Karemaker, Valentijn; Marques, Sophie; Sijsling, Jeroen is a scholarly article available to read on EtoBox.

What is Cubic Function Fields with Prescribed Ramification about?

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 explicit procedure to obtain a defining equation when the purely cubic closure $K'/K$ of $L/K$ is of 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 M\"obius transformations on $K$. The article concludes by studying the more general case of covers of elliptic and hyperelliptic curves that are ramified above exactly one point.

Author

Karemaker, Valentijn; Marques, Sophie; Sijsling, Jeroen

Published

2020

Language

EN