{
  "abstract": "Let $A$ be a ring, let ${\\bf T}$ be a finite-term big tilting complex over $A$, and choose a bounded projective representative $\\cpx{P}$ of ${\\bf T}$. Put $B=\\End_{\\D{A}}(\\cpx{P})$. We prove that the kernel of the associated derived tensor functor ${\\bf R}:\\D{B}\\to\\D{A}$ is equivalent, through the derived inclusion, to $\\D{\\mathscr E}$, where $\\mathscr E=\\Ker({\\bf R})\\cap B\\Modcat$ carries the inherited exact structure. Consequently, $\\D{B}$ admits a recollement by $\\D{\\mathscr E}$ and $\\D{A}$. The proof combines a dg double-centralizer argument with a functorial realisation of the kernel on unbounded complexes. The category $\\mathscr E$ is definable and $d$-symmetric whenever $d$ is at least the projective amplitude of the underlying perfect right $B$-complex. We also characterise when the kernel is induced by a homological ring epimorphism: this holds precisely when $\\mathscr E$ is an abelian subcategory, or equivalently when the standard $t$-structure restricts to the kernel. In amplitude at most one, this recovers the universal-localisation description for two-term big tilting complexes. Over semiperfect endomorphism rings, the amplitude is detected by reduction modulo the Jacobson radical. Finally, we construct non-compact examples of arbitrarily large minimal projective amplitude. One family yields algebraic Calkin quotients; another, over connected rings constructed from singular local hypersurfaces, has nonzero, non-abelian exact kernels and cannot be obtained from modules by derived equivalences between ordinary rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19921",
  "author_total": 2,
  "authors": [
    {
      "name": "Shengyong Pan"
    },
    {
      "name": "Huabo Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56zbzn2q19nxj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19921",
  "fulltext_url": null,
  "id": "56zbzn2q19nxj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19921",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7203877126",
  "pdf_url": "https://arxiv.org/pdf/2608.19921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56zbzn2q19nxj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2608.19921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Recollements of derived categories from $n$-term big tilting complexes",
  "title_text": "Recollements of derived categories from n-term big tilting complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/56zbzn2q19nxj",
  "venue": "arXiv",
  "versions": []
}