Polynomial factorization over henselian fields
Maria Alberich‐Carramiñana, Jordi Guàrdia, Enric Nart, Adrien Poteaux, Joaquím Roé, Martin Weimann · arXiv (Cornell University) · 2022
Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the factorization of $g$ over a henselization of $(K,v)$.