Indices of inseparability in towers of field extensions

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=apν. The indices of inseparability i0,i1,…,iν 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” ϕL/Kj for 0≤j≤ν. In this paper we give an interpretation of the values ϕL/Kj(c) for nonnegative integers c. We use this interpretation to study the behavior of generalized Hasse-Herbrand functions in towers of field extensions.