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arXiv · 1705.10433

Explicit reciprocity laws for higher local fields

Jorge Flórez
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Abstract

Using the previously constructed explicit 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.

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Jorge Flórez. 2020-01-17. Explicit reciprocity laws for higher local fields. https://doi.org/10.1016/j.jnt.2019.12.016

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