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arXiv · 2111.02811

Okutsu frames of irreducible polynomials over henselian fields

Maria Alberich-Carramiñana·Jordi Guàrdia·Joaquím Roé·Enric Nart
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Abstract

For a henselian valued field $(K,v)$ we establish a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F$ on $K[x]$, encoded by their MacLane-Vaqui\'e chains. This parallelism was only known for defectless irreducible polynomials.

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Maria Alberich-Carramiñana, Jordi Guàrdia, Joaquím Roé, Enric Nart. 2021-11-04. Okutsu frames of irreducible polynomials over henselian fields. https://arxiv.org/abs/2111.02811

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