On wild extensions of a p-adic field
Number Theory
2017-05-26 v1
Abstract
In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field, restricting to the case of extensions without intermediate fields. We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of Gal(F/K). Finally, for k = 2 and for each possible Galois group G, we count the number of isomorphism classes of the extensions whose normal closure has a Galois group isomorphic to G. As a byproduct, we get the total number of isomorphism classes.
Keywords
Cite
@article{arxiv.1601.05939,
title = {On wild extensions of a p-adic field},
author = {I. Del Corso and R. Dvornicich and M. Monge},
journal= {arXiv preprint arXiv:1601.05939},
year = {2017}
}