整体函数域的Tame类域理论
Tame Class Field Theory for Global Function Fields
摘要：
给出了函数域具体的、类域理论的主要结果关于度互素的阿贝尔扩张的特征的代数证明。通过采用一些已知的数域的方法，并以一种新的方式将它们结合起来，我们得到了一个不同的和简化得多的证明，它直接建立在函数域理论的标准基础知识上。我们的方法是明确的和建设性的，因此相关的算法应用。我们使用广义形式的Tate-Lichtenbaum和Ate配对，这是众所周知的密码学，作为一个重要的工具。
英文摘要：
We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way, we obtain a different and much simplified proof, which builds directly on a standard basic knowledge of the theory of function fields. Our methods are explicit and constructive and thus relevant for algorithmic applications. We use generalized forms of the Tate-Lichtenbaum and Ate pairings, which are well-known in cryptography, as an important tool.
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