{
  "abstract": "For a locally finitely generated Grothendieck category, we characterise the Gorenstein injective covering property by several equivalent conditions, including closure under coproducts. To complete this characterisation, we construct a countable commutative Noetherian Cohen--Macaulay local ring of dimension one for which this property fails, answering negatively Iacob's question Question 1 whether character modules of Gorenstein injective modules over left Noetherian rings are Gorenstein flat. Using this characterisation, we prove that for Noetherian schemes the covering property is Zariski-local. Moreover, assuming that $\\mathcal{GI}(\\mathrm{QCoh}(X))$ is a covering class, we establish compatible adjunctions and recollements for homotopy categories of injectives and totally acyclic injective complexes under open restriction. However, this property is not stalk-local: we construct a commutative Noetherian ring $S$ such that $\\mathcal{GI}(S_{\\mathfrak{p}})$ forms a covering class for all prime ideals $\\mathfrak{p}$, but $\\mathcal{GI}(S)$ do not form a covering class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18620",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuhui Hua"
    },
    {
      "name": "Shun-Jie Li"
    },
    {
      "name": "Chencheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63gwbkk5drtkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18620",
  "fulltext_url": null,
  "id": "63gwbkk5drtkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18620",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221787209",
  "pdf_url": "https://arxiv.org/pdf/2610.18620",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63gwbkk5drtkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18620",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18620"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the existence of Gorenstein injective covers",
  "title_text": "On the existence of Gorenstein injective covers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/63gwbkk5drtkf",
  "venue": "arXiv",
  "versions": []
}