A criterion for Lubin's conjecture

TL;DR

This paper establishes a criterion linking Lubin's conjecture on commuting power series to Galois extensions in nonarchimedean dynamics, leading to a new proof of the conjecture in specific cases.

Contribution

It introduces a new criterion equating Lubin's conjecture with Galois extension conditions, enabling a proof in previously unverified cases.

Findings

The conjecture is equivalent to a Galois extension criterion.

A new case of Lubin's conjecture is proved using this criterion.

The approach connects dynamical systems with Galois theory.

Abstract

We prove that a formulation of a conjecture of Lubin regarding two power series commuting for the composition is equivalent to a criterion of checking that some extensions generated by the nonarchimedean dynamical system arising from the power series are Galois. As a consequence of this criterion, we obtain a proof of Lubin's conjecture in a new case.