This paper studies the function field of an algebraic curve over an arbitrary perfect field by using the Weil reciprocity law and topologies on the adele ring. A topological subgroup of the idele class group is introduced and it is shown how it encodes arithmetic properties of the base field and of the Picard group of the curve. These results are applied to study extensions of the function field.

中文翻译：

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与韦尔互惠和皮卡德群有关的理想商

本文利用韦尔互易定律和阿黛尔环上的拓扑研究任意理想场上代数曲线的函数场。介绍了idele类组的一个拓扑子组，并显示了它如何编码基场和曲线的Picard组的算术属性。这些结果被应用于研究功能领域的扩展。