{
  "abstract": "Let A , B be dual abelian varieties. Let B ♮ $B^{\\natural }$ upper B Superscript normal ♮ be the universal vectorial extension of B . Laumon and Rothstein independently lift the Fourier–Mukai transform to D A $D_A$ upper D Subscript upper A -modules. They prove that this defines an equivalence of triangulated categories from the derived category D coh b ( D A ) $D_{\\mathrm {coh}}^b(D_A)$ upper D Subscript coh Superscript b Baseline left parenthesis upper D Subscript upper A Baseline right parenthesis of coherent D A $D_A$ upper D Subscript upper A -modules to the derived category D coh b ( O B ♮ ) $D_{\\mathrm {coh}}^b(O_{B^{\\natural }})$ upper D Subscript coh Superscript b Baseline left parenthesis upper O Subscript upper B Sub Superscript normal ♮ Subscript Baseline right parenthesis of coherent sheaves on B ♮ $B^{\\natural }$ upper B Superscript normal ♮ . We extend their results to complex tori. As a replacement of coherent algebraic D -modules, we use Kashiwara’s good analytic D -modules. Moreover, to get an equivalence, we have to replace O B ♮ $O_{B^{\\natural }}$ upper O Subscript upper B Sub Superscript normal ♮ by a commutative O B $O_B$ upper O Subscript upper B -algebra, which is locally a polynomial algebra over O B $O_B$ upper O Subscript upper B . As an application, we recover the Matsushima–Morimoto theorem that on a complex torus, a vector bundle admits a connection if and only if it is translation invariant, and in this case, it admits an integrable connection. Moreover, we use the Laumon–Rothstein transform to show that the derived category D h b ( D A ) $D_h^b(D_A)$ upper D Subscript h Superscript b Baseline left parenthesis upper D Subscript upper A Baseline right parenthesis of holonomic D -modules is a rigid symmetric monoidal triangulated category under the convolution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Haohao Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jsnebkjyxk9m.bib",
  "cited_by": 0,
  "doi": "10.1017/nmj.2026.10119",
  "fulltext_url": null,
  "id": "4jsnebkjyxk9m",
  "issns": [
    "0027-7630"
  ],
  "landing_url": "https://hal.science/hal-05736535v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7167600317",
  "pdf_url": "https://hal.science/hal-05736535/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-07",
  "publisher": "Duke University Press",
  "ris": "https://research.draconitic.com/paper/4jsnebkjyxk9m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05736535",
      "source": "hal",
      "url": "https://hal.science/hal-05736535v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fourier–Mukai transform for sheaves with connection on complex tori",
  "title_text": "Fourier–Mukai transform for sheaves with connection on complex tori",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:27Z",
  "url": "https://research.draconitic.com/paper/4jsnebkjyxk9m",
  "venue": "Nagoya Mathematical Journal",
  "versions": []
}