{
  "id": "finite-symmetric-tensor-categories-and-the-verlinde-tower",
  "title": "Finite symmetric tensor categories and the Verlinde tower",
  "description": "Every finite symmetric tensor category in characteristic p > 0 admits a fibre functor to a higher Verlinde category, the finite case of the Benson-Etingof-Ostrik conjecture, after OpenAI's 2026 manuscript. Tilting modules for SL_2; an equivariant vector bundle on the plane and the restricted tilting theorem; higher Frobenius functors; norm maps and symmetrizers; rank varieties; descent through Frobenius-Perron dimensions; incompressible categories and reconstruction.",
  "units": [
    {
      "id": "finite-symmetric-tensor-categories-and-fibre-functors",
      "title": "Finite symmetric tensor categories and fibre functors",
      "reader": "finite-symmetric-tensor-categories-and-fibre-functors.html",
      "source": "src/finite-symmetric-tensor-categories-and-fibre-functors.md",
      "source_sha256": "a03cc8a4796c9898a833c6609201ab8065238d7c0a0a3ffa9812d54bac5aeb93",
      "status": "author_self_checked"
    },
    {
      "id": "rational-representations-of-sl2-and-tilting-modules",
      "title": "Rational representations of SL₂ and tilting modules",
      "reader": "rational-representations-of-sl2-and-tilting-modules.html",
      "source": "src/rational-representations-of-sl2-and-tilting-modules.md",
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      "status": "author_self_checked"
    },
    {
      "id": "lifting-representations-of-elementary-abelian-groups-to-the-plane",
      "title": "Lifting representations of elementary abelian groups to the plane",
      "reader": "lifting-representations-of-elementary-abelian-groups-to-the-plane.html",
      "source": "src/lifting-representations-of-elementary-abelian-groups-to-the-plane.md",
      "source_sha256": "69a6074bae2de3803eb7a38364575411beb8c794c9331b5963960564fefd42b2",
      "status": "author_self_checked"
    },
    {
      "id": "the-restricted-tilting-theorem",
      "title": "The restricted tilting theorem",
      "reader": "the-restricted-tilting-theorem.html",
      "source": "src/the-restricted-tilting-theorem.md",
      "source_sha256": "f058826e0933ebe6b3c332d7682934df5dba1b5b66ba2ee5029d9df52f8c5f74",
      "status": "author_self_checked"
    },
    {
      "id": "higher-frobenius-functors",
      "title": "Higher Frobenius functors",
      "reader": "higher-frobenius-functors.html",
      "source": "src/higher-frobenius-functors.md",
      "source_sha256": "42268f3585295c9d96fd70cecc69ec20e7ebd3b341537b0cb2456c1297182b23",
      "status": "author_self_checked"
    },
    {
      "id": "norm-maps-and-a-first-nonprojective-tensor-power",
      "title": "Norm maps and a first nonprojective tensor power",
      "reader": "norm-maps-and-a-first-nonprojective-tensor-power.html",
      "source": "src/norm-maps-and-a-first-nonprojective-tensor-power.md",
      "source_sha256": "16cd65e36b19f5304f198e47eae8d2fb8dbdd4da0fd60069564d5ece76390f11",
      "status": "author_self_checked"
    },
    {
      "id": "rank-varieties-and-an-exact-higher-frobenius-functor",
      "title": "Rank varieties and an exact higher Frobenius functor",
      "reader": "rank-varieties-and-an-exact-higher-frobenius-functor.html",
      "source": "src/rank-varieties-and-an-exact-higher-frobenius-functor.md",
      "source_sha256": "606cdd16928947de05b38ffc5554c4ba1b47741216a9b3bf3c2499319d6057d0",
      "status": "author_self_checked"
    },
    {
      "id": "descent-to-a-verlinde-category",
      "title": "Descent to a Verlinde category",
      "reader": "descent-to-a-verlinde-category.html",
      "source": "src/descent-to-a-verlinde-category.md",
      "source_sha256": "632a07d7dff8e8df180eec2adc66366056ae0211f744e53f6aa6fc6d85f48448",
      "status": "author_self_checked"
    },
    {
      "id": "incompressible-categories-uniqueness-and-reconstruction",
      "title": "Incompressible categories, uniqueness and reconstruction",
      "reader": "incompressible-categories-uniqueness-and-reconstruction.html",
      "source": "src/incompressible-categories-uniqueness-and-reconstruction.md",
      "source_sha256": "f6b5352deb4720634c209fed00da55926c14e39671e527c76a1dabe84ef74547",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "rigid symmetric tensor categories, fibre functors and neutral Tannakian reconstruction (course The affine Grassmannian and geometric Satake, GL-SAT-09 Tannakian categories)",
    "representations of sl(2) in characteristic zero, for comparison (course Semisimple Lie algebras, RT-LIE-05)",
    "representations of finite groups, induced representations and Frobenius reciprocity (course Representations of finite groups)",
    "finite-dimensional algebras and modules, the Jacobson radical, Nakayama's lemma",
    "coherent sheaves and vector bundles on varieties, duals of coherent sheaves"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}