Computing the Galois group of a polynomial over a p-adic field

2020/03/12 by Doris, Christopher · 1 citation
#11S20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.05834

Abstract

We present a family of algorithms for computing the Galois group of a polynomial defined over a p-adic field. Apart from the "naive" algorithm, these are the first general algorithms for this task. As an application, we compute the Galois groups of all totally ramified extensions of ℚ₂ of degrees 18, 20 and 22, tables of which are available online.

Cited by

• Families of p-adic fields

Related

• Explicit computation of Galois p-groups unramified at p
• Combinatorial Techniques in the Galois Theory of p-Extensions
• Finding Galois splitting models to compute local invariants
• Computing finite Galois groups arising from automorphic forms
• Enumerating Extensions of (π)-Adic Fields with Given Invariants