Galois scaffolds for extraspecial p-extensions in characteristic 0

Abstract

Let K be a local field of characteristic 0 with residue characteristic $p>2$. Let G be an extraspecial p-group and let $L/K$ be a totally ramified G-extension. In this paper we find sufficient conditions for $L/K$ to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers $O_L$ to be free of rank 1 over its associated order $A_{L/K}$, and to stricter conditions which imply that $A_{L/K}$ is a Hopf order in the group ring $K\left[G\right]$.