{
  "id": "1411.1191",
  "version": "v1",
  "published": "2014-11-05T08:53:22.000Z",
  "updated": "2014-11-05T08:53:22.000Z",
  "title": "An explicit formula for the generic number of dormant indigenous bundles",
  "authors": [
    "Yasuhiro Wakabayashi"
  ],
  "comment": "28 pages",
  "journal": "Publ. Res. Inst. Math. Sci. 50 (2014), pp. 383-409",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "A dormant indigenous bundle is an integrable projective line bundle on a proper hyperbolic curve of positive characteristic satisfying certain conditions. Dormant indigenous bundles were introduced and studied in the $p$-adic Teichmuller theory developed by S. Mochizuki. Kirti Joshi proposed a conjecture concerning an explicit formula for the degree over the moduli stack of curves of the moduli stack classifying dormant indigenous bundles. In this paper, we give a proof for this conjecture of Joshi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-05T08:53:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H60"
    ],
    "keywords": [
      "explicit formula",
      "generic number",
      "proper hyperbolic curve",
      "stack classifying dormant indigenous bundles",
      "moduli stack classifying dormant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1191W"
    }
  }
}