{
  "id": "2209.09392",
  "version": "v1",
  "published": "2022-09-20T00:26:01.000Z",
  "updated": "2022-09-20T00:26:01.000Z",
  "title": "Ind-étale vs Formally étale",
  "authors": [
    "Shubhodip Mondal",
    "Alapan Mukhopadhyay"
  ],
  "comment": "13 pages. Comments welcome",
  "categories": [
    "math.AG",
    "math.AC",
    "math.KT",
    "math.RA"
  ],
  "abstract": "We show that when $A$ is a reduced algebra over a characteristic zero field $k$ and the module of K\\\"ahler differentials $\\Omega_{A/k}=0$, then $A$ is ind-\\'etale, partially answering a question of Bhatt. As further applications of this result, we deduce a rigidity property of Hochschild homology and special instances of Weibel's conjecture and Vorst's conjecture without any noetherian assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-20T00:26:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B25",
      "13B40",
      "19D99",
      "16E40"
    ],
    "keywords": [
      "characteristic zero field",
      "noetherian assumptions",
      "rigidity property",
      "special instances",
      "weibels conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}