{
  "id": "2207.02033",
  "version": "v1",
  "published": "2022-07-05T13:22:42.000Z",
  "updated": "2022-07-05T13:22:42.000Z",
  "title": "Hilbert-Samuel formula and positivity over adelic curves",
  "authors": [
    "Huayi Chen",
    "Atsushi Moriwaki"
  ],
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We establish, in the setting of Arakelov geometry over adelic curves, an arithmetic Hilbert-Samuel theorem describing the asymptotic behaviour of the metrized graded linear series of an adelic line bundle in terms of its arithmetic intersection number. We then study positivity conditions of adelic line bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-05T13:22:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40",
      "11G50"
    ],
    "keywords": [
      "adelic curves",
      "hilbert-samuel formula",
      "adelic line bundle",
      "arithmetic hilbert-samuel theorem",
      "arithmetic intersection number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}