One-dimensional elementary abelian extensions have Galois scaffolding
Number Theory
2007-05-23 v2
Abstract
We define a variant of normal basis, called a {\em Galois scaffolding}, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local function fields of characteristic , called {\em one-dimensional}, that, in a particular sense, are as simple as cyclic degree extensions, and prove the statement in the title above.
Cite
@article{arxiv.math/0511174,
title = {One-dimensional elementary abelian extensions have Galois scaffolding},
author = {G. Griffith Elder},
journal= {arXiv preprint arXiv:math/0511174},
year = {2007}
}
Comments
13 pages. This is a revision of "One-dimensional elementary-abelian extensions of local fields," which is being split into two papers. This paper restricts itself to local fields of characteristic $p$ and proves a stronger result than in the original