%0 Journal Article
%T Determination of the number of isomorphism classes of extensions of a $\kp$-adic field
%A Maurizio Monge
%J Mathematics
%D 2010
%I arXiv
%X We deduce a formula enumerating the isomorphism classes of extensions of a $\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula follows from a simple group-theoretic lemma, plus the Krasner formula and an elementary class field theory computation. It shows that the number of classes only depends on the ramification and inertia of the extensions $K/\Q_p$, and $K(\zeta_{p^m})/K$ obtained adding the $p^m$-th roots of 1, for all $p^m$ dividing $e$.
%U http://arxiv.org/abs/1011.0357v3