{
  "id": "1908.10064",
  "version": "v1",
  "published": "2019-08-27T07:43:07.000Z",
  "updated": "2019-08-27T07:43:07.000Z",
  "title": "Model Theory of Proalgebraic Groups",
  "authors": [
    "Anand Pillay",
    "Michael Wibmer"
  ],
  "comment": "39 pages",
  "categories": [
    "math.LO",
    "math.AG",
    "math.CT"
  ],
  "abstract": "We lay the foundations for a model theoretic study of proalgebraic groups. Our axiomatization is based on the tannakian philosophy. Through a tensor analog of skeletal categories we are able to consider neutral tannakian categories with a fibre functor as many-sorted first order structures. The class of diagonalizable proalgebraic groups is analyzed in detail. We show that the theory of a diagonalizable proalgebraic group $G$ is determined by the theory of the base field and the theory of the character group of $G$. Some initial steps towards a comprehensive study of types are also made.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-27T07:43:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "03C65",
      "14L15",
      "14L17",
      "20G05",
      "18D10"
    ],
    "keywords": [
      "model theory",
      "diagonalizable proalgebraic group",
      "neutral tannakian categories",
      "model theoretic study",
      "many-sorted first order structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}