{
  "abstract": "Let $p$ be a fixed prime number and let $R$ be a $p$-quasisyntomic ring. We provide conditions for objects in the absolute prismatic site $R_\\Prism$ to cover the final object in $\\Shv(R_\\Prism)$ and to admit finite self-coproducts in $R_\\Prism$. More precisely, we introduce in $R_\\Prism$ the so-called transversal objects, so that the coproduct of any object in $R_\\Prism$ with a transversal object exists in $R_\\Prism$. As an immediate generalization, we introduce the so-called relatively quasiregular semiperfectoid covers of $R$, whose prismatic cohomology (of $δ$-pairs, in the sense of Antieau-Krause-Nikolaus) produces objects in $R_\\Prism$ that cover the final object in $\\Shv(R_\\Prism)$ and admit finite self-coproducts in $R_\\Prism$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04931",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingbang Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9z3khz8cg124d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04931",
  "fulltext_url": null,
  "id": "9z3khz8cg124d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04931",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7167598507",
  "pdf_url": "https://arxiv.org/pdf/2607.04931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9z3khz8cg124d.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:28Z",
      "native_id": "2607.04931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A note on prismatic sites for p-quasisyntomic rings",
  "title_text": "A note on prismatic sites for p-quasisyntomic rings",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/9z3khz8cg124d",
  "venue": "arXiv",
  "versions": []
}