Indices of inseparability in towers of field extensions

2014/02/21 by Keating, Kevin
#11S15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1402.5193

Abstract

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^ν. The indices of inseparability i₀,i₁,...,i_ν 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" ϕ_L/K^j for 0≤ j≤ν. In this paper we give an interpretation of the values ϕ_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.

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