Galois scaffolds for extraspecial p-extensions in characteristic 0
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917731982376960 |
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| author | Keating, Kevin Schwartz, Paul |
| author_facet | Keating, Kevin Schwartz, Paul |
| contents | 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 $K[G]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galois scaffolds for extraspecial p-extensions in characteristic 0 Keating, Kevin Schwartz, Paul Number Theory 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 $K[G]$. |
| title | Galois scaffolds for extraspecial p-extensions in characteristic 0 |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.17355 |