{
  "id": "1609.03187",
  "version": "v1",
  "published": "2016-09-11T17:32:33.000Z",
  "updated": "2016-09-11T17:32:33.000Z",
  "title": "Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over $\\mathbb{Z}_p$",
  "authors": [
    "Jishnu Ray"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is a general principle that objects coming from semi-simple, simply connected (split) groups have explicit presentations like Serre's presentation of semi-simple algebras and Steinberg's presentation of Chevalley groups. In this paper we give an explicit presentation (by generators and relations) of the Iwasawa algebra for the first congruence kernel of a semi-simple, simply connected Chevalley group over $\\mathbb{Z}_p$, extending the proof given by Clozel for the group $\\Gamma_1(SL_2(\\mathbb{Z}_p))$, the first congruence kernel of $SL_2(\\mathbb{Z}_p)$ for primes $p>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-11T17:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "22E35",
      "22E50"
    ],
    "keywords": [
      "first congruence kernel",
      "simply connected chevalley group",
      "iwasawa algebra",
      "explicit presentation",
      "general principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}