{
  "id": "math/0604232",
  "version": "v2",
  "published": "2006-04-11T03:10:45.000Z",
  "updated": "2006-04-13T13:09:43.000Z",
  "title": "Local-global principles for representations of quadratic forms",
  "authors": [
    "Jordan Ellenberg",
    "Akshay Venkatesh"
  ],
  "comment": "TeX clash causing O to appear as \\emptyset fixed",
  "doi": "10.1007/s00222-007-0077-7",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension $\\geq 7$. The proof uses the ergodic theory of $p$-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-13T13:09:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic forms",
      "representations",
      "local-global principle holds",
      "integral points",
      "adic groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2007,
      "month": "Nov",
      "volume": 171,
      "number": 2,
      "pages": 257
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InMat.171..257E"
    }
  }
}