arXiv Analytics

Sign in

arXiv:1803.08023 [math.NT]AbstractReferencesReviewsResources

On enumerating extensions of p-adic fields with given invariants

Christopher Doris

Published 2018-03-21Version 1

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.

Comments: 15 pages; code available from https://cjdoris.github.io/pAdicExtensions
Categories: math.NT
Related articles: Most relevant | Search more
arXiv:1504.06671 [math.NT] (Published 2015-04-24)
Enumerating Extensions of $(π)$-Adic Fields with Given Invariants
arXiv:1902.00699 [math.NT] (Published 2019-02-02)
Dilogarithm and higher $\mathscr{L}$-invariants for $\mathrm{GL}_3(\mathbb{Q}_p)$
arXiv:1105.5221 [math.NT] (Published 2011-05-26, updated 2011-09-04)
An ultrametric space of Eisenstein polynomials and ramification theory

Links

Toolbox