Okutsu frames of irreducible polynomials over henselian fields

2021/11/04 by Maria Alberich‐Carramiñana, Jordi Guàrdia, Alberich-Carramiñana, Maria +5
Computer Science · Engineering · Mathematics · #Polynomial and algebraic computation #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2111.02811

Abstract

For a henselian valued field (K,v) we establish a complete parallelism between the arithmetic properties of irreducible polynomials F∈ 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-Vaquié chains. This parallelism was only known for defectless irreducible polynomials.

Related

• Okutsu sequences in Henselian fields
• Invariants of algebraic elements over henselian fields
• Valuative trees over valued fields
• On chains associated with abstract key polynomials
• Polynomial factorization over henselian fields