Families of p-adic fields

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

Families of p-adic fields

Number Theory 2025-07-04 v1

Authors: Jordi Guàrdia Rúbies , John W. Jones , Kevin Keating , Sebastian Pauli , David P. Roberts , David Roe

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 $n \leq 23$ .

Keywords

p-adic fields Krasner-Monge polynomials LMFDB degree n extensions database

Cite

@article{arxiv.2507.02360,
  title  = {Families of p-adic fields},
  author = {Jordi Guàrdia Rúbies and John W. Jones and Kevin Keating and Sebastian Pauli and David P. Roberts and David Roe},
  journal= {arXiv preprint arXiv:2507.02360},
  year   = {2025}
}

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27 pages

Families of p-adic fields

Abstract

Keywords

Cite

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