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arXiv · 2507.02360

Families of p-adic fields

Jordi Guàrdia Rúbies·John W. Jones·Kevin Keating·Sebastian Pauli·David P. Roberts·David Roe
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Abstract

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 $n \leq 23$.

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Jordi Guàrdia Rúbies, John W. Jones, Kevin Keating, Sebastian Pauli, David P. Roberts, David Roe. 2025-07-03. Families of p-adic fields. https://arxiv.org/abs/2507.02360

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