{
  "abstract": "Let $A=\\mathbb{Q}[t^{\\frac{1}{2^n}}:n\\geq 0]$ and consider $A[u,u^{-1};σ]$, a skew Laurent polynomial ring, where $σ(t^q)=t^{2q}$. We study the kernel of derived extension of scalars along $ A[u,u^{-1};σ]\\longrightarrow\\mathbb{Q}[u,u^{-1}], $ the quotient by $\\mathfrak{m}A[u,u^{-1};σ]$, with $\\mathfrak{m}=(t^{\\frac{1}{2^n}}:n\\geq 0)$. A finite free resolution of $\\mathfrak{m}A[u,u^{-1};σ]$ over $ A[u,u^{-1};σ]\\otimes_{\\mathbb{Q}} \\bigl(A[u,u^{-1};σ]\\bigr)^{\\mathrm{op}} $ proves smoothness. A specialization inequality for matrix ranks supplies a nonzero exact colimit-preserving functor that vanishes on every compact object, proving failure of compact generation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14874",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Frolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7c3vd7n5j254g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14874",
  "fulltext_url": null,
  "id": "7c3vd7n5j254g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14874",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221791603",
  "pdf_url": "https://arxiv.org/pdf/2610.14874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7c3vd7n5j254g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A smooth non-compactly generated category",
  "title_text": "A smooth non-compactly generated category",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7c3vd7n5j254g",
  "venue": "arXiv",
  "versions": []
}