{
  "abstract": "FINDING: Geometric Langlands correspondence is being actively constructed via moduli stacks of local systems and Hecke eigensheaves, with recent advances by Gaitsgory, Raskin, and others toward a full categorical formulation. | MATH: The correspondence conjecturally identifies the derived category of coherent sheaves on the moduli stack of local systems \\( \\mathrm{LocSys}_G(\\Sigma) \\) with the derived category of D-modules on the moduli stack of principal \\( G \\)-bundles \\( \\mathrm{Bun}_G(\\Sigma) \\), for a smooth projective curve \\( \\Sigma \\). Key objects: Hecke eigensheaves — D-modules \\( \\mathcal{F} \\) on \\( \\mathrm{Bun}_G \\) satisfying \\( H_\\mu(\\mathcal{F}) \\cong \\mathcal{F} \\boxtimes \\sigma_\\mu(\\mathcal{E}) \\) for each Hecke correspondence, where \\( \\sigma_\\mu \\) is the representation of the Langlands dual group \\( {}^L G \\) with highest weight \\( \\mu \\). The local version (Braverman) involves affine Grassmannian \\( \\mathrm{Gr}_G = G(\\mathbb{C}((t)))/G(\\mathbb{C}[[t]]) \\) and its c\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67gm0bdvtdy8h.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553976",
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  "id": "67gm0bdvtdy8h",
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  "landing_url": "https://zenodo.org/records/23553976",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67gm0bdvtdy8h.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:15Z",
      "native_id": "23553976",
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      "url": "https://zenodo.org/records/23553976"
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  "subjects": [],
  "title": "Geometric Langlands: Categorical Formulation via Moduli Stacks and Hecke Eigensheaves — E8 Intelligence Research",
  "title_text": "Geometric Langlands: Categorical Formulation via Moduli Stacks and Hecke Eigensheaves — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:15Z",
  "url": "https://research.draconitic.com/paper/67gm0bdvtdy8h",
  "venue": "Zenodo",
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}