Defectless polynomials over henselian fields and inductive valuations

2019/03/15 by de Oliveira, Nathália Moraes, Nart, Enric
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1903.06736

Abstract

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

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