{
  "id": "2505.07044",
  "version": "v1",
  "published": "2025-05-11T16:32:57.000Z",
  "updated": "2025-05-11T16:32:57.000Z",
  "title": "On definable groups in dp-minimal topological fields equipped with a generic derivation",
  "authors": [
    "Françoise Point"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $T$ be a complete, model-complete, geometric dp-minimal $\\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\\partial)$ be the theory of expansions of models of $T$ by a derivation $\\partial$. We assume that $T(\\partial)$ has a model-companion $T_{\\partial}$. Let $\\Gamma$ be a finite-dimensional $\\mathcal{L}_\\partial$-definable group in a model of $T_\\partial$. Then we show that $\\Gamma$ densely and definably embeds in an $\\mathcal{L}$-definable group $G$. Further, using a $C^1$-cell decomposition result, we show that $\\Gamma$ densely and definably embeds in a definable $D$-group, generalizing the classical construction of Buium of algebraic $D$-groups and extending for that class of fields, results obtained in arXiv:2208.08293, arXiv:2305.16747.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-11T16:32:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "12H05",
      "12L12"
    ],
    "keywords": [
      "definable group",
      "dp-minimal topological fields",
      "generic derivation",
      "definably embeds",
      "cell decomposition result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}