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Galois scaffolds for extraspecial p-extensions in characteristic 0 (2407.17355v1)
Published 24 Jul 2024 in math.NT
Abstract: Let $K$ be a local field of characteristic 0 with residue characteristic $p$. 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 $\mathfrak{O}L$ to be free of rank 1 over its associated order $\mathfrak{A}{L/K}$, and to stricter conditions which imply that $\mathfrak{A}_{L/K}$ is a Hopf order in the group ring $K[G]$.