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arXiv · 1903.06736

Defectless polynomials over henselian fields and inductive valuations

Nathália Moraes de Oliveira·Enric Nart
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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 $v$.

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Nathália Moraes de Oliveira, Enric Nart. 2019-03-15. Defectless polynomials over henselian fields and inductive valuations. https://arxiv.org/abs/1903.06736

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