One-dimensional elementary abelian extensions have Galois scaffolding
Abstract
Description
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.
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
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