# Explicit reciprocity laws for higher local fields

## TL;DR

This paper extends explicit reciprocity laws to higher local fields using Lubin-Tate formal groups, providing a detailed description of the Kummer pairing via multidimensional p-adic differentiation, generalizing classical formulas.

## Contribution

It offers a new explicit description of the Kummer pairing for higher local fields, generalizing classical reciprocity laws with a focus on Lubin-Tate formal groups.

## Key findings

- Explicit formulas for Kummer pairing in higher local fields
- Generalization of Artin-Hasse, Iwasawa, Kolyvagin, and Wiles formulas
- Application of multidimensional p-adic differentiation

## 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.