Families of p-adic fields
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909674585980928 |
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| author | Rúbies, Jordi Guàrdia Jones, John W. Keating, Kevin Pauli, Sebastian Roberts, David P. Roe, David |
| author_facet | Rúbies, Jordi Guàrdia Jones, John W. Keating, Kevin Pauli, Sebastian Roberts, David P. Roe, David |
| contents | We improve the database of $p$-adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize $p$-adic fields into families. They thereby make long lists of fields more manageable and various theoretical structures more evident. In particular, the database now includes all degree $n$ extensions of $\mathbb{Q}_p$, for $p<200$ and $n \leq 23$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of p-adic fields Rúbies, Jordi Guàrdia Jones, John W. Keating, Kevin Pauli, Sebastian Roberts, David P. Roe, David Number Theory 11S15 (primary), 11F85, 11S05, 11S20, 11Y40, 12F05 (secondary) We improve the database of $p$-adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize $p$-adic fields into families. They thereby make long lists of fields more manageable and various theoretical structures more evident. In particular, the database now includes all degree $n$ extensions of $\mathbb{Q}_p$, for $p<200$ and $n \leq 23$. |
| title | Families of p-adic fields |
| topic | Number Theory 11S15 (primary), 11F85, 11S05, 11S20, 11Y40, 12F05 (secondary) |
| url | https://arxiv.org/abs/2507.02360 |