{
  "id": "2106.15038",
  "version": "v1",
  "published": "2021-06-29T00:33:55.000Z",
  "updated": "2021-06-29T00:33:55.000Z",
  "title": "On the arithmetic Siegel--Weil formula for GSpin Shimura varieties",
  "authors": [
    "Chao Li",
    "Wei Zhang"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We formulate and prove a local arithmetic Siegel--Weil formula for GSpin Rapoport--Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport--Zink spaces and the derivatives of local representation densities of quadratic forms. As a first application, we prove a semi-global arithmetic Siegel--Weil formula as conjectured by Kudla, which relates the arithmetic intersection numbers of special cycles on GSpin Shimura varieties at a place of good reduction and the central derivatives of nonsingular Fourier coefficients of incoherent Siegel Eisenstein series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T00:33:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gspin shimura varieties",
      "gspin rapoport-zink spaces",
      "arithmetic intersection numbers",
      "semi-global arithmetic siegel-weil formula",
      "local arithmetic siegel-weil formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}