Hopf-Galois module structure of degree p extensions of p-adic fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909013759754240 |
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| author | Gil-Muñoz, Daniel |
| author_facet | Gil-Muñoz, Daniel |
| contents | Let $p$ be an odd prime number. For a degree $p$ extension of $p$-adic fields $L/K$, we give a complete characterization of the condition for the ring of integers $\mathcal{O}_L$ to be free as a module over its associated order in the unique Hopf-Galois structure on $L/K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf-Galois module structure of degree p extensions of p-adic fields Gil-Muñoz, Daniel Number Theory Let $p$ be an odd prime number. For a degree $p$ extension of $p$-adic fields $L/K$, we give a complete characterization of the condition for the ring of integers $\mathcal{O}_L$ to be free as a module over its associated order in the unique Hopf-Galois structure on $L/K$. |
| title | Hopf-Galois module structure of degree p extensions of p-adic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.10383 |