Parametrization of Formal Norm Compatible Sequences

TL;DR

This paper classifies power series that parametrize Lubin-Tate trace compatible sequences, generalizing classical results and providing explicit methods for special cases, thus advancing understanding in Iwasawa theory and local class field theory.

Contribution

It offers a classification of parametrizing power series for Lubin-Tate sequences and extends Coleman's interpolation theorem to a broader context.

Findings

Classified power series parametrizing Lubin-Tate sequences

Generalized Coleman's interpolation theorem

Provided explicit methods for special cases

Abstract

We give a classification of power series parametrizing Lubin-Tate trace compatible sequences. This proof answers a question posed in the literature by Berger and Fourquaux. Lubin-Tate trace compatible sequences are a generalization of norm compatible sequences, which arise in Iwasawa theory and local class field theory. The result we prove generalizes the interpolation theorem proved by Coleman in the classical norm compatible sequence case. We also, jointly with Victor Kolyvagin, give a method for finding such series explicitly in certain special cases.