{
  "id": "1911.00614",
  "version": "v1",
  "published": "2019-11-01T23:39:43.000Z",
  "updated": "2019-11-01T23:39:43.000Z",
  "title": "A Counterexample to the $φ$-Dimension Conjecture",
  "authors": [
    "Eric J. Hanson",
    "Kiyoshi Igusa"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In 2005, the second author and Todorov introduced an upper bound on the finitistic dimension of an Artin algebra, now known as the $\\phi$-dimension. The $\\phi$-dimension conjecture states that this upper bound is always finite, a fact that would imply the finitistic dimension conjecture. In this paper, we present a counterexample to the $\\phi$-dimension conjecture and explain where it comes from. We also discuss implications for further research and the finitistic dimension conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-01T23:39:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E05",
      "16E10",
      "16G10",
      "16G20",
      "18G20"
    ],
    "keywords": [
      "finitistic dimension conjecture",
      "counterexample",
      "upper bound",
      "dimension conjecture states",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}