Indices of inseparability in towers of field extensions

Kevin Keating

Published 2014-02-21, updated 2015-01-08Version 2

Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=ap^{\nu}$. The indices of inseparability $i_0,i_1,...,i_{\nu}$ of $L/K$ were defined by Fried in the case char$(K)=p$ and by Heiermann in the case char$(K)=0$; they give a refinement of the usual ramification data for $L/K$. The indices of inseparability can be used to construct "generalized Hasse-Herbrand functions" $\phi_{L/K}^j$ for $0\le j\le\nu$. In this paper we give an interpretation of the values $\phi_{L/K}^j(c)$ for natural numbers $c$. We use this interpretation to study the behavior of generalized Hasse-Herbrand functions in towers of field extensions.