English

Okutsu frames of irreducible polynomials over henselian fields

Commutative Algebra 2023-03-24 v2

Abstract

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

Keywords

Cite

@article{arxiv.2111.02811,
  title  = {Okutsu frames of irreducible polynomials over henselian fields},
  author = {Maria Alberich-Carramiñana and Jordi Guàrdia and Joaquím Roé and Enric Nart},
  journal= {arXiv preprint arXiv:2111.02811},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2107.09813