{
  "abstract": "Let $M$ be a silting object in an idempotent complete algebraic triangulated category $\\mathcal T$. Put $B={\\rm End}_{\\mathcal T}(M)$, and let $\\mathbb{P}_M\\colon {\\rm pr}(M)\\to K^{[-1,0]}({\\rm proj}B)$ be the presentation functor associated with $M$. It was recently asked whether $\\mathbb{P}_M(T)$ must be tilting whenever $T\\in{\\rm pr}(M)$ is a tilting object. We answer this question in the negative by giving an explicit finite-dimensional example. Namely, for $$ Λ=k(1\\xrightarrowα2\\xrightarrowβ3\\xrightarrowγ4)/(αβγ),$$ we construct a silting object $M\\in K^b({\\rm proj}Λ)$ and a tilting object $T=ΣΛ\\in{\\rm pr}(M)$ for which $$ {\\rm dim}_k{\\rm Hom}_{K^b({\\rm proj}B)}\\bigl(\\mathbb{P}_M(T),Σ^{-1}\\mathbb{P}_M(T)\\bigr)=1.$$ Thus $\\mathbb{P}_M(T)$ is a two-term silting complex but not a tilting complex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02023",
  "author_total": 2,
  "authors": [
    {
      "name": "Jing He"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63pbe8w894j88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02023",
  "fulltext_url": null,
  "id": "63pbe8w894j88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02023",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7207860195",
  "pdf_url": "https://arxiv.org/pdf/2609.02023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63pbe8w894j88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A negative answer to a question on tilting objects and two-term complexes",
  "title_text": "A negative answer to a question on tilting objects and two-term complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/63pbe8w894j88",
  "venue": "arXiv",
  "versions": []
}