{
  "id": "2012.07365",
  "version": "v2",
  "published": "2020-12-14T09:31:18.000Z",
  "updated": "2023-01-13T09:50:30.000Z",
  "title": "The trivial fiber topology and framed motives over the integers",
  "authors": [
    "A. Druzhinin",
    "Håkon Kolderup",
    "Paul Arne Østvær"
  ],
  "comment": "Revised version, with new results",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the Garkusha-Panin and Voevodsky strict $\\mathbb{A}^{1}$-invariance theorems to one-dimensional base schemes. The trivial fiber topology plays a central role in the proof of refined localization results for motivic homotopy categories. Moreover, we extend Morel's $\\mathbb{A}^{1}$-connectivity theorem on Nisnevich sheaves of stable motivic homotopy groups. These results open new vistas for computations of motivic invariants over deeper base schemes of arithmetic interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-01-13T09:50:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "framed motives",
      "motivic homotopy category",
      "one-dimensional base schemes",
      "stable motivic homotopy",
      "motivic infinite loop spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}