{
  "id": "2004.12172",
  "version": "v1",
  "published": "2020-04-25T15:39:29.000Z",
  "updated": "2020-04-25T15:39:29.000Z",
  "title": "Local Constancy of Intersection Numbers",
  "authors": [
    "Andreas Mihatsch"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We prove that, in certain situations, intersection numbers on formal schemes that come in profinite families vary locally constantly in the parameter. To this end, we define the product $S\\times M$ of a profinite set $S$ with a locally noetherian formal scheme $M$ and study intersections thereon. Our application is to the Arithmetic Fundamental Lemma of W. Zhang where the result helps to remove a restriction in its recent proof, cf. arXiv:1909.02697.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-25T15:39:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C17",
      "11G18"
    ],
    "keywords": [
      "intersection numbers",
      "local constancy",
      "locally noetherian formal scheme",
      "profinite families vary",
      "study intersections thereon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}