{
  "id": "0704.2030",
  "version": "v1",
  "published": "2007-04-16T17:38:22.000Z",
  "updated": "2007-04-16T17:38:22.000Z",
  "title": "New Approach to Arakelov Geometry",
  "authors": [
    "Nikolai Durov"
  ],
  "comment": "568 pages, with hyperlinks",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct such an approach we develop a theory of generalized rings and schemes, which include classical rings and schemes together with \"exotic\" objects such as F_1 (\"field with one element\"), Z_\\infty (\"real integers\"), T (tropical numbers) etc., thus providing a systematic way of studying such objects. This theory of generalized rings and schemes is developed up to construction of algebraic K-theory, intersection theory and Chern classes. Then existence of Arakelov models of algebraic varieties over Q is shown, and our general results are applied to such models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-16T17:38:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40",
      "14A20",
      "18G55",
      "08A40"
    ],
    "keywords": [
      "arakelov geometry",
      "generalized rings",
      "general results",
      "algebraic approach",
      "real integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 568,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.2030D"
    }
  }
}