Galois scaffolds and semistable extensions

Abstract

Let $K$ be a local field and let $L/K$ be a totally ramified Galois extension of degree $p^n$. Being semistable and possessing a Galois scaffold are two conditions which facilitate the computation of the additive Galois module structure of $L/K$. In this note we show that $L/K$ is semistable if and only if $L/K$ has a Galois scaffold. We also give sufficient conditions in terms of Galois scaffolds for the extension $L/K$ to be stable.