{
  "schema_version": 1,
  "problem_number": "AIM-ALGEBRAIC_GEOMETRY-0162",
  "title": "Infinitesimal Lifting Does Not Imply Flatness for Green Functors",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let k be any nonzero commutative ring of characteristic two. The ghost map from the constant C2-Tambara functor on k is finitely presented and has unique lifting against square-zero extensions, but is not flat for the relative Mackey box product. Its two orbit maps are the finite etale ring maps k to k x k and k to k, and both its Green and genuine Tambara differential modules vanish. An explicit monomorphism of modules acquires a nonzero top-supported kernel after tensoring. The ghost construction is known and is attributed to existing literature; the note applies it to the lifting-versus-flatness question in the 2016 AIM workshop report on equivariant derived algebraic geometry. It distinguishes infinitesimal lifting from Hill's flatness-based definition of formal etaleness. The broader derived geometry problem is not resolved. This is an AI-assisted, self-audited, unrefereed preprint with no absolute priority claim.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.AT",
    "math.AG",
    "math.AC"
  ],
  "keywords": [
    "Green functor",
    "Tambara functor",
    "infinitesimal lifting",
    "Mackey box product",
    "ghost construction",
    "AIM-ALGEBRAIC_GEOMETRY-0162"
  ],
  "manuscript_version_date": "2026-10-18",
  "publication_date": "2026-10-18",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-18",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0162/",
  "pdf_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0162/paper.pdf?v=ff5da79fd9cb",
  "doi": "10.5281/zenodo.23448648",
  "zenodo_record_url": "https://zenodo.org/records/23448648",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The complete counterexample refutes the specific lifting-implies-flatness assertion in the official AIM workshop report, even under finite presentation and orbitwise finite etaleness. The ghost construction is known and credited. It does not contradict definitions that require flatness, nor resolve the whole open-ended Green/Tambara geometry source record. AI-assisted, self-audited and unrefereed; no independent review, proof-assistant certification or absolute-priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "ff5da79fd9cb915a8fe04358eb451bd6198df067be0d417900eaf3f9b3339c8d"
    },
    "source.zip": {
      "sha256": "0700c576395257fe4020da8925f2bb1b08d425296517ab7d82e4d76708eefd82"
    },
    "verification_report.md": {
      "sha256": "86229f81155eddd55814b7bd29f3c33e3ea2a31b2a2e2c0996447b9b7d2ff71f"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}