Galois scaffolding in one-dimensional elementary abelian extensions

Abstract

A Galois scaffold is defined to be a variant of a normal basis that allows for an easy determination of valuation and thus has implications for the questions of the Galois module structure. We introduce a class of elementary abelian p p -extensions of local function fields of characteristic p p , which we call one-dimensional and which should be considered no more complicated than cyclic degree p p extensions, and show that they, just as cyclic degree p p extensions, possess a Galois scaffold.