Families of p-adic fields

2025/07/03 by Rúbies, Jordi Guàrdia, Jones, John W., Keating, Kevin +3 · 1 citation
#11F85 #11S05 #11S15 (primary) #11S20 #11Y40 #12F05 (secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.02360

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 ℚ_p, for p<200 and n ≤ 23.

Citations

• Computing the Galois group of a polynomial over a p-adic field
• Jump sets in local fields
• Enumerating Extensions of (π)-Adic Fields with Given Invariants
• A family of Eisenstein polynomials generating totally ramified\n extensions, identification of extensions and construction of class fields
• Determination of the number of isomorphism classes of extensions of a \kp-adic field

Cited by

• On inertial types of elliptic curves

Related

• Counting Extensions of \mathfrakp-Adic Fields with Given Invariants
• Enumerating Extensions of (π)-Adic Fields with Given Invariants
• Determination of the number of isomorphism classes of extensions of a \kp-adic field
• An identification for Eisenstein polynomials over a p-adic field
• On Classifying Extensions of p-adic Fields