{
  "abstract": "Let $\\mathcal{T}$ be a tensor triangulated category with a compact tilting generator $M$ and abelian heart $\\mathcal{H}_M = M^{\\bot_{\\neq0}}$. We define a triangulated flat dimension $\\mathrm{flatdim}_{\\mathcal{T}}X$ for $X\\in\\mathcal{T}$, and give criteria in terms of tensor vanishing and resolutions by the class of pure quotients of $\\mathrm{Add}(M)$. We further introduce $M$-ghost length and $M$-ghost dimension, and show that the global dimension of $\\mathcal{H}_M$ controls the $M$-ghost length of all objects in $\\mathcal{T}$, and that the $M$-ghost dimension of $\\mathcal{T}$ coincides with the weak global dimension of $\\mathcal{H}_M$ and the supremum of $\\mathrm{flatdim}_{\\mathcal{T}}X+\\mathrm{inf}X$ of bounded objects, and the relative triangulated dimension of $\\mathcal{T}^c$ with respect to $\\mathrm{add}(M)$. This extends the classical Hovey-Lockridge theorem, which is recovered for derived categories of rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14420",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaoyan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bm0qxvxa70rnz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14420",
  "fulltext_url": null,
  "id": "bm0qxvxa70rnz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14420",
  "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.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221753492",
  "pdf_url": "https://arxiv.org/pdf/2610.14420",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bm0qxvxa70rnz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14420",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14420"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Flat and Ghost dimensions in tensor triangulated categories with a compact tilting generator",
  "title_text": "Flat and Ghost dimensions in tensor triangulated categories with a compact tilting generator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/bm0qxvxa70rnz",
  "venue": "arXiv",
  "versions": []
}