On Lubin-Tate regulator maps and Kato's explicit reciprocity law

TL;DR

This paper extends the Lubin-Tate regulator map to Artin characters and establishes a reciprocity law, providing a new proof of Kato's explicit reciprocity law for Lubin-Tate formal groups.

Contribution

It generalizes the interpolation property of the Lubin-Tate regulator map and offers a novel proof of Kato's explicit reciprocity law.

Findings

Extended the Lubin-Tate regulator map to Artin characters.

Proved a reciprocity law in the sense of Cherbonnier-Colmez.

Provided a new proof of Kato's explicit reciprocity law.

Abstract

We extend the interpolation property of the Lubin-Tate regulator map from [SV24] to Artin characters and show a reciprocity law in the sense of Cherbonnier-Colmez. This allows us to provide a new proof of Kato's explicit reciprocity law for Lubin-Tate formal groups.