{
  "abstract": "For any translation invariant generalized complex structure J on a torus we construct the derived category D(J) generalizing the derived category of coherent sheaves on a complex torus and the affine/convergent Fukaya category of a symplectic torus. The category is defined in terms of a non-commutative curved deformation of the Dolbeault algebra of a complex torus. We show that this category is independent of the chosen deformation path, which we prove using non-commutative Fourier-Mukai duality. We also prove that the action of O(2n,2n; Z) on the space of generalized complex structures leaves the category D(J) invariant. In particular, T-duality acts trivially on D(J). We construct concrete objects associated to affine Lagrangians in the derived category associated to a symplectic torus and show that their spaces of morphisms are given by Floer cohomology. We show that our construction is consistent with the homological mirror symmetry conjecture (including its non-commutative version).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21960",
  "author_total": 5,
  "authors": [
    {
      "name": "Patrick Antweiler"
    },
    {
      "name": "Vicente Cortés"
    },
    {
      "name": "Julian Holstein"
    },
    {
      "name": "Markus Röser"
    },
    {
      "name": "Aldo Witte"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7x1twyzxea8n0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21960",
  "fulltext_url": null,
  "id": "7x1twyzxea8n0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21960",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222546651",
  "pdf_url": "https://arxiv.org/pdf/2610.21960",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7x1twyzxea8n0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21960",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21960"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The derived category of a generalized complex torus",
  "title_text": "The derived category of a generalized complex torus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7x1twyzxea8n0",
  "venue": "arXiv",
  "versions": []
}