{
  "abstract": "Let $V$ be a complete valuation domain of rank 1, and let $Γ$ be its value group. We investigate the power series ring $V[[t]]$, and finally answer the long standing question of when this ring is coherent. Specifically, we prove that it is coherent if and only if $V$ is almost maximal, and either $Γ= \\mathbb{R}$ or $Γ$ is discrete. Furthermore, we demonstrate that the weak Hilbert-syzygy identity $w. dim V [[X]] = w. dim V + 1$ holds if and only if $V[[X]]$ is a coherent ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05246",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohamed Amine Aouichaoui"
    },
    {
      "name": "Adam Jones"
    },
    {
      "name": "Yiding Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj4a8ggevz3h4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05246",
  "fulltext_url": null,
  "id": "bj4a8ggevz3h4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05246",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj4a8ggevz3h4.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Coherence and the Hilbert-syzygy identity for power series over valuation domains",
  "title_text": "Coherence and the Hilbert-syzygy identity for power series over valuation domains",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/bj4a8ggevz3h4",
  "venue": "arXiv",
  "versions": []
}