{
  "abstract": "We study ramification invariants of finite separable extensions of valued fields that are pure on a primitive element. In the immediate unibranched case, we prove that the extended trace ideal is generated by minimal-polynomial derivatives of integral primitive elements and that the Dedekind different is its divisorial closure. For Galois extensions, we express this derivative ideal as a product of subgroup ramification ideals. These formulas extend prime-degree calculations to pure extensions of higher degree. We compute the differential module, traces, differents, ramification ideals, and character Swan ideals of a pure immediate elementary abelian extension of degree $p^2$. A totally ramified example of the same degree gives a comparison with the defectless case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03909",
  "author_total": 1,
  "authors": [
    {
      "name": "Josnei Novacoski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fs8ym79yatyvy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03909",
  "fulltext_url": null,
  "id": "fs8ym79yatyvy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03909",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220736039",
  "pdf_url": "https://arxiv.org/pdf/2610.03909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fs8ym79yatyvy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ramification invariants of pure extensions",
  "title_text": "Ramification invariants of pure extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/fs8ym79yatyvy",
  "venue": "arXiv",
  "versions": []
}