{
  "abstract": "Let $W$ be a henselian valuation ring with fraction field $L$, residue field $k$, and value group $Γ_W$. Let $N=\\ell^ν$ be invertible in $W$. Choose an ordered $\\mathbf Z/N$-basis $B$ of $Γ_W/NΓ_W$. Products of suitable classes define an equivalence of complete filtered spectra $$ \\bigoplus_{\\substack{J\\subseteq B\\\\J\\text{ finite}}} Σ^{|J|}\\operatorname{Fil}_{\\mathrm{mot}}^{\\bullet-|J|} K(k;\\mathbf Z/N) \\xrightarrow{\\simeq} \\operatorname{Fil}_{\\mathrm{mot}}^{\\bullet} K(L;\\mathbf Z/N) $$ The summand indexed by $\\varnothing$ is the generic restriction map, after the rigidity equivalence $K(W;\\mathbf Z/N)\\simeq K(k;\\mathbf Z/N)$, and is therefore split injective. Independently of this splitting, excision yields a lifting theorem for regular henselian pairs. In particular, this yields finite-coefficient Gersten injectivity for noetherian henselian regular local rings. Applications to completions along regular primes give relative and sometimes nonhenselian examples. More generally, if $P$ is a Prüfer ring and $R$ is a henselian local ind-smooth $P$-algebra, then $R$ is a domain and $K_n(R;\\mathbf Z/N)\\to K_n(\\operatorname{Frac}(R);\\mathbf Z/N)$ is injective for every $n$, provided $N\\in R^\\times$. These injectivity consequences extend from prime-power to arbitrary finite invertible coefficients by primary decomposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18789",
  "author_total": 1,
  "authors": [
    {
      "name": "Niels Feld"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10yxjj47rkwwh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18789",
  "fulltext_url": null,
  "id": "10yxjj47rkwwh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18789",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7203887079",
  "pdf_url": "https://arxiv.org/pdf/2608.18789",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10yxjj47rkwwh.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2608.18789",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18789"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite-coefficient K-theory of henselian valued fields and Gersten injectivity",
  "title_text": "Finite-coefficient K-theory of henselian valued fields and Gersten injectivity",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/10yxjj47rkwwh",
  "venue": "arXiv",
  "versions": []
}