{
  "abstract": "Let $K$ be a field, and $\\mathcal{T}$ a $K$-linear essentially small triangulated category equipped with an extendable $t$-structure $(\\mathcal{T}^{\\leq0}, \\mathcal{T}^{\\geq0})$ with respect to a good metric $\\mathfrak{B}$. Given a torsion class $\\mathcal{X}$ in the heart of $(\\mathcal{T}^{\\leq0}, \\mathcal{T}^{\\geq0})$, we prove that lifting the HRS-tilt of $(\\mathcal{T}^{\\leq0}, \\mathcal{T}^{\\geq0})$ at $\\mathcal{X}$ along the completion of $\\mathcal{T}$ coincides with the HRS-tilt of the lifted $t$-structure at the completion of $\\mathcal{X}$. As an application, we provide the compatibility result between left silting mutation in $\\mathcal{T}$ and HRS tilting in the ambient completion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13699",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiaojiao Lu"
    },
    {
      "name": "Zhongkui Liu"
    },
    {
      "name": "Renyu Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ctbtrake68mw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13699",
  "fulltext_url": null,
  "id": "3ctbtrake68mw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13699",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13699",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ctbtrake68mw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13699",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13699"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Compatibility of HRS tilt and completion of $t$-structures in triangulated categories",
  "title_text": "Compatibility of HRS tilt and completion of t-structures in triangulated categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3ctbtrake68mw",
  "venue": "arXiv",
  "versions": []
}