{
  "id": "1901.02870",
  "version": "v1",
  "published": "2019-01-09T18:44:31.000Z",
  "updated": "2019-01-09T18:44:31.000Z",
  "title": "Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas",
  "authors": [
    "Xuhua He",
    "Chao Li",
    "Yihang Zhu"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We prove a character formula for some closed fine Deligne-Lusztig varieties. We apply it to compute fixed points for fine Deligne-Lusztig varieties arising from the basic loci of Shimura varieties of Coxeter type. As an application, we prove an arithmetic intersection formula for certain diagonal cycles on unitary and GSpin Rapoport-Zink spaces arising from the arithmetic Gan-Gross-Prasad conjectures. In particular, we prove the arithmetic fundamental lemma in the minuscule case, without assumptions on the residual characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-09T18:44:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G17",
      "20G40"
    ],
    "keywords": [
      "arithmetic fundamental lemma",
      "arithmetic gan-gross-prasad conjectures",
      "gspin rapoport-zink spaces",
      "closed fine deligne-lusztig varieties",
      "arithmetic intersection formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}