Finding Galois splitting models to compute local invariants

For prime p and small n, Jones and Roberts have developed a database recording invariants for p-adic extensions of degree n. We contributed to this database by computing the Galois slope content, Galois mean slope, and inertia subgroup for a variety of wildly ramified extensions of composite degree...

Full description

Saved in:
Bibliographic Details
Published in:Journal of number theory Vol. 261; pp. 241 - 251
Main Author: Carrillo, Benjamin
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2024
Subjects:
Galois groups
Generic Polynomials
Inverse Galois Theory
Local fields
Panayi's Root Finding Algorithm
Inverse Galois Theory
Local fields
Galois groups
Generic Polynomials
Panayi's Root Finding Algorithm
ISSN:0022-314X, 1096-1658
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For prime p and small n, Jones and Roberts have developed a database recording invariants for p-adic extensions of degree n. We contributed to this database by computing the Galois slope content, Galois mean slope, and inertia subgroup for a variety of wildly ramified extensions of composite degree using the idea of Galois splitting models. We will describe a number of strategies to find Galois splitting models including an original technique using generic polynomials and Panayi's root finding algorithm.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2024.02.010