{
  "abstract": "It is an unfortunate fact that even over commutative noetherian rings, localization of K-injective complexes need not be K-injective. However, not all is lost. Given a complex of injective modules $J$ over a commutative noetherian ring $A$, we show that K-injectivity of $J$ can be detected locally: if $(A,\\mathfrak{m})$ is a noetherian local ring, then $J$ is K-injective over $A$ if and only if $\\operatorname{Hom}_A(\\widehat{A},J)$ is K-injective over $\\widehat{A}$, the $\\mathfrak{m}$-adic completion of $A$; and for an arbitrary commutative noetherian ring $A$, $J$ is K-injective over $A$ if and only if $\\operatorname{Hom}_A(A_{\\mathfrak{m}},J)$ is K-injective over $A_{\\mathfrak{m}}$ for every maximal ideal $\\mathfrak{m}$ in the singular locus of $A$. The local result is deduced from a more general theorem on faithfully flat descent of K-injectivity along maps to (possibly noncommutative, possibly non-noetherian) rings. The global result is established via the local-to-global principle in tensor-triangulated geometry. As an application, we generalize a theorem of Grothendieck on faithfully flat descent of regularity, extending it to faithfully flat extensions by noncommutative left coherent left regular rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05884",
  "author_total": 1,
  "authors": [
    {
      "name": "Liran Shaul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvt9n5gejwwxv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05884",
  "fulltext_url": null,
  "id": "cvt9n5gejwwxv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05884",
  "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",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7220691520",
  "pdf_url": "https://arxiv.org/pdf/2610.05884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvt9n5gejwwxv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "K-injective complexes in commutative algebra",
  "title_text": "K-injective complexes in commutative algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cvt9n5gejwwxv",
  "venue": "arXiv",
  "versions": []
}