Galois scaffolds for cyclic $p^n$-extensions in characteristic $p$

DOI10.1007/S40993-022-00381-2arXiv2201.08885MaRDI QIDQ6388860

Gove Griffith Elder, Kevin Keating

Publication date: 21 January 2022

Abstract: Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified Galois extension such that Gal$(L/K)cong{C}_{p^n}$. 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 $A_0$, and to stricter conditions which imply that $A_0$ is a Hopf order in the group ring $K[C_{p^n}]$.

Mathematics Subject Classification ID

Galois theory (11S20) Ramification and extension theory (11S15)

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