Defectless polynomials over henselian fields and inductive valuations

Abstract

Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.