Explicit local reciprocity for tame extensions

TL;DR

This paper provides an explicit formula for the local reciprocity map in tamely ramified abelian extensions of local fields of degree n, without requiring the base field to contain nth roots of unity.

Contribution

It introduces a new explicit formula for local reciprocity in tamely ramified abelian extensions without the roots of unity assumption.

Findings

Explicit formula for local reciprocity map derived

Applicable to tamely ramified abelian extensions of local fields

Removes the need for nth roots of unity in the base field

Abstract

We consider a tamely ramified abelian extension of local fields of degree n, without assuming the presence of the nth roots of unity in the base field. We give an explicit formula which computes the local reciprocity map in this situation.