Galois scaffolds for extraspecial p-extensions in characteristic 0
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 $K[G]$.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.17355
- arXiv:
- arXiv:2407.17355
- Bibcode:
- 2024arXiv240717355K
- Keywords:
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- Mathematics - Number Theory