{
  "abstract": "Let $V$ be a complete discrete valuation ring of mixed characteristic $(0,3)$ in which $3$ is a uniformizer, and put $A=V[[x,y]]/(3+x^2-y^3)$. We construct a nonzero class $a\\in K_2(A;\\mathbf Z/3)$ whose restriction to the fraction field of $A$ is zero. Thus Gersten injectivity for algebraic $K$-theory with $\\mathbf Z/3$-coefficients fails for a two-dimensional ramified regular local ring. We also indicate the expected analogous construction for every odd prime. This counterexample does not contradict the integral Gersten conjecture but it rules out a naive reduction to finite coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.05005",
  "author_total": 1,
  "authors": [
    {
      "name": "Niels Feld"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dapyj0hwv41ye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.05005",
  "fulltext_url": null,
  "id": "dapyj0hwv41ye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.05005",
  "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.KT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7196944763",
  "pdf_url": "https://arxiv.org/pdf/2608.05005",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dapyj0hwv41ye.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2608.05005",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.05005"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite-coefficient Gersten injectivity fails in ramified mixed characteristic",
  "title_text": "Finite-coefficient Gersten injectivity fails in ramified mixed characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/dapyj0hwv41ye",
  "venue": "arXiv",
  "versions": []
}