{
  "abstract": "We extend quasi-projective dimension and quasi-projective length from finitely generated modules to homologically finite complexes by using finite filtrations in the derived category. Our definitions recover the original invariants of Gheibi--Jorgensen--Takahashi for modules and behave well under exact functors, which simplifies the proofs of several results. We establish the Auslander--Buchsbaum formula, the derived depth and width formulas, and the dependency formula for complexes of finite quasi-projective dimension. Extending a result of Gheibi--Jorgensen--Takahashi, we show that every homologically finite complex has finite quasi-projective dimension over a suitable complete intersection ring. We also prove a new intersection theorem and a descent theorem for Serre's conditions. Finally, we obtain vanishing results for Tor, Ext, and Tate (co)homology, and also symmetry of eventual Ext vanishing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23289",
  "author_total": 1,
  "authors": [
    {
      "name": "Hiroki Matsui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44kr4me72j582.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23289",
  "fulltext_url": null,
  "id": "44kr4me72j582",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23289",
  "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": "W7214003126",
  "pdf_url": "https://arxiv.org/pdf/2609.23289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44kr4me72j582.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.23289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-projective dimension for complexes via filtrations",
  "title_text": "Quasi-projective dimension for complexes via filtrations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/44kr4me72j582",
  "venue": "arXiv",
  "versions": []
}