{
  "id": "1705.05167",
  "version": "v1",
  "published": "2017-05-15T11:41:06.000Z",
  "updated": "2017-05-15T11:41:06.000Z",
  "title": "Remarks on the arithmetic fundamental lemma",
  "authors": [
    "Chao Li",
    "Yihang Zhu"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space. In the minuscule case, Rapoport-Terstiege-Zhang have verified the AFL conjecture via explicit evaluation of both sides of the identity. We present a simpler way for evaluating the arithmetic intersection number, thereby providing a new proof of the AFL conjecture in the minuscule case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-15T11:41:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G18",
      "14G17",
      "22E55"
    ],
    "keywords": [
      "arithmetic intersection number",
      "afl conjecture",
      "minuscule case",
      "zhangs arithmetic fundamental lemma",
      "unitary rapoport-zink space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}