{
  "abstract": "We study the extension of valuations centered in a local domain to its henseliza-tion. We prove that a valuation ν centered in a local domain R uniquely determines a minimal prime H(ν) of the henselization R h of R and an extension of ν centered in R h /H(ν), which has the same value group as ν. Our method, which assumes neither that R is noetherian nor that it is integrally closed, is to reduce the problem to the extension of the valuation to a quotient of a standard étale local R-algebra and in that situation to draw valuative consequences from the observation that the Newton-Hensel algorithm for constructing roots of polynomials produces sequences that are always pseudo-convergent in the sense of Ostrowski. We then apply this method to the study of the approximation of elements of the henselization of a valued field by elements of the field and give a characterization of the henselian property of a local domain (R, m R) in terms of the limits of certain pseudo-convergent sequences of elements of m R for a valuation centered in it. Another consequence of our work is to establish in full generality a bijective correspondence between the minimal primes of the henselization of a local domain R and the connected components of the Riemann-Zariski space of valuations centered in R.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "1903.10793",
  "author_total": 2,
  "authors": [
    {
      "name": "Ana Belén de Felipe Paramio"
    },
    {
      "name": "Bernard H Teissier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xanaw0manpqa.bib",
  "cited_by": 0,
  "doi": "10.1007/s0028-020-01970-1",
  "fulltext_url": null,
  "id": "9xanaw0manpqa",
  "issns": [
    "0025-5831",
    "1432-1807"
  ],
  "landing_url": "https://hal.science/hal-02077611v2",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ac"
    ],
    [
      "hal",
      "1.math.math-ag"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W2922577706",
  "pdf_url": "https://hal.science/hal-02077611/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/9xanaw0manpqa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-02077611",
      "source": "hal",
      "url": "https://hal.science/hal-02077611v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ac",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Valuations and henselization",
  "title_text": "Valuations and henselization",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:50Z",
  "url": "https://research.draconitic.com/paper/9xanaw0manpqa",
  "venue": "Mathematische Annalen",
  "versions": []
}