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