English

An elementary proof of the local Kronecker-Weber theorem

Number Theory 2026-05-27 v2

Abstract

We will present a novel elementary, self-contained, and explicit 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.

Keywords

Cite

@article{arxiv.2206.05801,
  title  = {An elementary proof of the local Kronecker-Weber theorem},
  author = {Jochen Koenigsmann and Benedikt Stock},
  journal= {arXiv preprint arXiv:2206.05801},
  year   = {2026}
}

Comments

16 pages, 1 figure