{
  "schema_version": 1,
  "problem_number": "AIM-ALGEBRAIC_GEOMETRY-0289",
  "title": "Presentation Independence of Ambient Adjoint Cartier Algebras",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let R=S/I be an integral algebra of finite type over a perfect field of characteristic p>0, with S polynomial and I of height c. We give a direct proof that restriction to R of degree-e Cartier maps with coefficients in I^{c(p^e-1)} is independent of the polynomial presentation, in every degree. A dummy-variable coefficient identity and common graph presentations compare arbitrary polynomial embeddings. Ideal-pair twists are independent of ambient lifts. The resulting Cartier algebras and their test ideals localize and glue without a Q-Gorenstein assumption. We explain the established comparison with Mather-Jacobian multiplier ideals for each fixed rational-exponent pair over an algebraically closed characteristic-zero field, after reduction to sufficiently general closed fibres.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "keywords": [
    "Cartier algebra",
    "test ideal",
    "adjoint ideal",
    "Mather-Jacobian multiplier ideal",
    "Frobenius trace",
    "presentation independence",
    "positive characteristic",
    "AIM-ALGEBRAIC_GEOMETRY-0289",
    "math.AC",
    "math.AG"
  ],
  "manuscript_version_date": "2026-10-03",
  "publication_date": "2026-10-03",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-03",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0289/",
  "pdf_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0289/paper.pdf?v=9e6530991cc8",
  "doi": "10.5281/zenodo.23115591",
  "zenodo_record_url": "https://zenodo.org/records/23115591",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of the polynomial-presentation and pair-lift independence theorem for integral finite-type algebras over perfect fields in positive characteristic, including localization and gluing. The ambient construction and rational-pair characteristic-zero reduction comparison are prior work of Takagi, Smolkin, Eisenstein and Ein-Ishii-Mustata. This addresses the MJ interpretation of AIM Problem 2.15 (AIM-ALGEBRAIC_GEOMETRY-0289), not all readings of that construction request. No pure-Mather theorem, all-small-prime resolution equality or imperfect-base generalization is claimed. The original source record is not counted as fully resolved. AI-assisted, self-audited and unrefereed; no independent human review or proof-assistant verification. Novelty remains undetermined; no absolute-priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "9e6530991cc88d93933112a236b8c59654c6161cc25b338207cc0acbfd685b60"
    },
    "source.zip": {
      "sha256": "461d486112e274d6c2fe92aa98902bb9f2b94952789ac038daf3f9be8d3aa788"
    },
    "verification_report.md": {
      "sha256": "7bde6c0b49a1b864ef8a2154cbaae91467a29d960a6ac5491f3c348fcb7dbc16"
    }
  },
  "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."
}