English

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.

Keywords

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

R2 v1 2026-06-23T01:00:41.551Z