{
  "id": "2106.03123",
  "version": "v1",
  "published": "2021-06-06T13:30:47.000Z",
  "updated": "2021-06-06T13:30:47.000Z",
  "title": "The $θ$-density on Arakelov geometry",
  "authors": [
    "Xiaozong Wang"
  ],
  "comment": "21 pages, comments welcome !",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this article, we construct a $\\theta$-density for the global sections of Hermitian line bundles on a projective arithmetic variety. We show that this density has similar behaviour to the usual density in the Arakelov geometric setting, where only global sections of norm smaller than $1$ are considered. In particular, we prove the analogue by $\\theta$-density of two Bertini kind theorems, on irreducibility and regularity respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-06T13:30:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arakelov geometry",
      "global sections",
      "hermitian line bundles",
      "bertini kind theorems",
      "similar behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}