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 $p$-extensions of local function fields of characteristic $p$, which we call one-dimensional and which should be considered no more complicated than cyclic degree $p$ extensions, and show that they, just as cyclic degree $p$ extensions, possess a Galois scaffold.