{
  "id": "2212.01901",
  "version": "v1",
  "published": "2022-12-04T19:33:27.000Z",
  "updated": "2022-12-04T19:33:27.000Z",
  "title": "Perfectoid Nullstellensatz: Results and counterexamples",
  "authors": [
    "Ian Gleason"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Abstract. We give necessary conditions and we give sufficient conditions for perfectoid Nullstellensatz to hold. As a consequence, we prove that perfectoid Nullstellensatz does not hold for $\\mathbb{C}_p$ and other natural p-adic fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-04T19:33:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfectoid nullstellensatz",
      "counterexamples",
      "natural p-adic fields",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}