论文标题
有规定的分支化的立方功能字段
Cubic function fields with prescribed ramification
论文作者
论文摘要
本文介绍了Cubic函数字段$ L/K $带有规定的RAMIFIENT，其中$ K $是一个合理的功能字段。我们给出了此类扩展的一般方程式，当纯粹的立方闭合$ k'/k $ of $ l/k $的明确程序以获得定义方程式，以及$ l/k $的曲折的描述，即$ l/k $，高于$ k $。对于属的立方功能字段，我们还描述了当允许$ k $上的möbius变换时获得的曲折和同构类。本文通过研究更普遍的椭圆形和全椭圆形曲线的覆盖案例，这些曲线恰好在一个点上方均被击中。
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 Möbius 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.
