On enumerating extensions of p-adic fields with given invariants
Number Theory
2018-03-22 v1
Abstract
We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons of Eisenstein polynomials over p-adic fields, their associated residual polynomials and an algorithm to produce all extensions for a given ramification polygon. We supplement this with an algorithm to produce all ramification polygons of a given degree, and hence we can produce all totally ramified extensions of a given degree.
Cite
@article{arxiv.1803.08023,
title = {On enumerating extensions of p-adic fields with given invariants},
author = {Christopher Doris},
journal= {arXiv preprint arXiv:1803.08023},
year = {2018}
}
Comments
15 pages; code available from https://cjdoris.github.io/pAdicExtensions