Defectless polynomials over henselian fields and inductive valuations

Abstract

Let $(K,v)$ be a henselian valued field. Let ${\mathbb{P}}^{dless}\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\approx$ on ${\mathbb{P}}^{dless}$, we establish a canonical bijection $\mathbb{M}\to {\mathbb{P}}^{dless}/\approx$, where $\mathbb{M}$ is a discrete MacLane space, constructed in terms of inductive valuations on $K[x]$ extending $v$.