论文标题
全球田地的基本阿贝尔延伸的属属和扩展属田地
Genus Field and Extended Genus Field of an Elementary Abelian Extension of Global Fields
论文作者
论文摘要
在目前的工作中，我们为属属领域的构建和基本的Abelian $ l $ l $延伸的扩展属领域扩展了一个理性功能，其中$ l $是质量数字。在Kummer案件中，如果$ k $包含在环形函数领域中，则使用Leopoldt的想法通过Dirichlet角色进行构造。遵循Anglès的定义和扩展希尔伯特阶级字段的jaulent，我们获得了一个理性功能领域的小学Abelian $ l $扩展的扩展属字段。
In the present work we give the construction of the genus field and the extended genus field of an elementary abelian $l$-extension of a field of rational functions, where $l$ is a prime number. In the Kummer case, if $K$ is contained in a cyclotomic funtion field, the construction is given using Leopoldt's ideas by means of Dirichlet characters. Following the definition of Anglès and Jaulent of extended Hilbert class field, we obtain the extended genus field of an elementary abelian $l$-extension of a field of rational functions.
