{
  "id": "1907.06225",
  "version": "v1",
  "published": "2019-07-14T13:53:11.000Z",
  "updated": "2019-07-14T13:53:11.000Z",
  "title": "Pathological Behavior of Arithmetic Invariants of Unipotent Groups",
  "authors": [
    "Zev Rosengarten"
  ],
  "comment": "36 pages; This is the second half of a preprint arXiv:1806.10723 submitted earlier; we have broken it up in order to make the arXiv versions conform to the published ones",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that all of the nice behavior for Tamagawa numbers, Tate-Shafarevich sets, and other arithmetic invariants of pseudo-reductive groups over global function fields proved in \\cite{rospred} fails in general for non-commutative unipotent groups. We also give some positive results which show that Tamagawa numbers do exhibit some reasonable behavior for arbitrary connected linear algebraic groups over global function fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-14T13:53:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic invariants",
      "unipotent groups",
      "pathological behavior",
      "global function fields",
      "tamagawa numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}