Families of p-adic fields

TL;DR

This paper enhances the p-adic fields database by systematically organizing fields into families using Krasner-Monge polynomials, covering all degree n extensions of _p for primes less than 200 and degrees up to 23.

Contribution

It introduces a systematic method for classifying p-adic fields into families, improving database organization and theoretical clarity.

Findings

Includes all degree n extensions of _p for p<200 and n . 23.

Organizes p-adic fields into families for better manageability.

Makes theoretical structures more evident.

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 $n \leq 23$.