An Elementary Proof of the Local Kronecker-Weber Theorem

TL;DR

This paper provides a new elementary, self-contained proof of the local Kronecker-Weber theorem, avoiding advanced tools like local class field theory and Galois cohomology.

Contribution

It introduces a novel proof that relies only on basic algebraic concepts taught in undergraduate courses.

Findings

Proof is elementary and self-contained

Avoids advanced tools like local class field theory

Accessible to undergraduates

Abstract

We will present a novel elementary and self-contained proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on algebra. In particular, we will not make use of results from local class field theory or Galois cohomology.