{
  "id": "2409.04570",
  "version": "v1",
  "published": "2024-09-06T19:18:10.000Z",
  "updated": "2024-09-06T19:18:10.000Z",
  "title": "Globally valued fields: foundations",
  "authors": [
    "Itaï Ben Yaacov",
    "Pablo Destic",
    "Ehud Hrushovski",
    "Michał Szachniewicz"
  ],
  "comment": "51 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present foundations of globally valued fields, i.e., of a class of fields with an extra structure, capturing some aspects of the geometry of global fields, based on the product formula. We provide a dictionary between various data defining such extra structure: syntactic (models of some unbounded continuous logic theory), Arakelov theoretic, and measure theoretic. In particular we obtain a representation theorem relating globally valued fields and adelic curves defined by Chen and Moriwaki.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-06T19:18:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "foundations",
      "extra structure",
      "adelic curves",
      "theorem relating globally valued fields",
      "global fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}