Abstract Using previously constructed reciprocity laws for the generalized Kummer pairing of an arbitrary (one-dimensional) formal group, in this article a special consideration is given to Lubin-Tate formal groups. In particular, this allows for a completely explicit description of the Kummer pairing in terms of multidimensional p-adic differentiation. The results obtained here constitute a generalization, to higher local fields, of the formulas of Artin-Hasse, Iwasawa, Kolyvagin and Wiles.

中文翻译：

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高等局部域的显式互惠律

摘要 使用先前为任意（一维）形式群的广义 Kummer 配对构建的互易律，在本文中特别考虑了 Lubin-Tate 形式群。特别是，这允许根据多维 p-adic 微分对 Kummer 配对进行完全明确的描述。此处获得的结果构成了 Artin-Hasse、Iwasawa、Kolyvagin 和 Wiles 公式对更高局部域的推广。