{
  "id": "2404.17234",
  "version": "v1",
  "published": "2024-04-26T08:11:07.000Z",
  "updated": "2024-04-26T08:11:07.000Z",
  "title": "Generic differentiability and $P$-minimal groups",
  "authors": [
    "Will Johnson"
  ],
  "comment": "50 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove generic differentiability in $P$-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's $P$-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically, let $G$ be an $n$-dimensional definable group in a highly saturated model $M$ of a $P$-minimal theory. Then there is an open definable subgroup $H \\subseteq G$ such that $H$ is compactly dominated by $H/H^{00}$, and $H/H^{00}$ is a $p$-adic Lie group of the expected dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-26T08:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C60",
      "12L12"
    ],
    "keywords": [
      "generic differentiability",
      "minimal theory",
      "adic lie group",
      "open definable subgroup",
      "minimal analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}