{
  "id": "1702.03623",
  "version": "v1",
  "published": "2017-02-13T04:17:22.000Z",
  "updated": "2017-02-13T04:17:22.000Z",
  "title": "Connections on parahoric torsors over curves",
  "authors": [
    "Vikraman Balaji",
    "Indranil Biswas",
    "Yashonidhi Pandey"
  ],
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We define parahoric $\\cG$--torsors for certain Bruhat--Tits group scheme $\\cG$ on a smooth complex projective curve $X$ when the weights are real, and also define connections on them. We prove that a $\\cG$--torsor is given by a homomorphism from $\\pi_1(X\\setminus D)$ to a maximal compact subgroup of $G$, where $D\\, \\subset\\, X$ is the parabolic divisor, if and only if the torsor is polystable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-13T04:17:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14L30"
    ],
    "keywords": [
      "parahoric torsors",
      "bruhat-tits group scheme",
      "maximal compact subgroup",
      "smooth complex projective curve",
      "define parahoric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}