{
  "abstract": "We define semiorthogonal decompositions of stable $\\infty$-categories of length $n$, extending the theory of semiorthogonal decompositions presented in arXiv:2106.02873. Prior to this, we explicitly construct an equivalence of $\\infty$-categories relating Waldhausen diagrams to coherent complexes in stable $\\infty$-categories. This allows us to view semiorthogonal decompositions from two different perspectives, each of which has its unique advantages and disadvantages. Under mild conditions, we prove a reconstruction theorem for semiorthogonal decompositions, recovering a stable $\\infty$-category as the (op)lax limit of a diagram formed by the subcategories constituting its decomposition. We apply this reconstruction in the case of Beilinson's exceptional collection, to obtain a reconstruction of $D^b(\\text{Coh}(\\mathbb{P}^n))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31020",
  "author_total": 1,
  "authors": [
    {
      "name": "Rio Haeussler Albi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2yfsa6y9035q4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31020",
  "fulltext_url": null,
  "id": "2yfsa6y9035q4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.31020",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204925789",
  "pdf_url": "https://arxiv.org/pdf/2608.31020",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2yfsa6y9035q4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.31020",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31020"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Semiorthogonal decompositions of stable $\\infty$-categories",
  "title_text": "Semiorthogonal decompositions of stable ∞-categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2yfsa6y9035q4",
  "venue": "arXiv",
  "versions": []
}