Galois scaffolds and semistable extensions

Let K be a local field and let L/K be a totally ramified Galois extension of degree p(n). Being semistable [2] and possessing a Galois scaffold [4] 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. (C) 2019 Elsevier Inc. All rights reserved.