One-dimensional elementary abelian extensions have Galois scaffolding

2005/11/07 by G. Griffith Elder, Elder, G. Griffith
Mathematics · #11S15 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11S15

paper · pdf · doi:10.48550/arxiv.math/0511174

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

arxiv created 2007/05/02 · arxiv updated 2009/12/01

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 p, called \em one-dimensional, that, in a particular sense, are as simple as cyclic degree p extensions, and prove the statement in the title above.

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