{
  "id": "1404.2362",
  "version": "v2",
  "published": "2014-04-09T04:26:29.000Z",
  "updated": "2014-11-25T17:45:26.000Z",
  "title": "Reduction modulo $p$ of certain semi-stable representations",
  "authors": [
    "Chol Park"
  ],
  "comment": "34 pages, Contains minor correction from the previous version, Comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p>3$ be a prime number and let $G_{\\mathbb{Q}_p}$ be the absolute Galois group of $\\mathbb{Q}_p$. In this paper, we find Galois stable lattices in the irreducible $3$-dimensional semi-stable and non-crystalline representations of $G_{\\mathbb{Q}_p}$ with Hodge--Tate weights $(0,1,2)$ by constructing their strongly divisible modules. We also compute the Breuil modules corresponding to the mod $p$ reductions of the strongly divisible modules, and determine which of the semi-stable representations has an absolutely irreducible mod $p$ reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-09T04:26:29.000Z",
      "abstract": "Let $p>3$ be a prime number and let $G_{\\mathbb{Q}_p}$ be the absolute Galois group of $\\mathbb{Q}_p$. In this paper, we find Galois stable lattices in the irreducible $3$-dimensional semi-stable representations of $G_{\\mathbb{Q}_p}$ with Hodge--Tate weights $(0,1,2)$ by constructing their strongly divisible modules. We also compute the Breuil modules corresponding to the mod $p$ reductions of the strongly divisible modules, and determine which of the semi-stable representations has an absolutely irreducible mod $p$ reduction.",
      "comment": "34 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-25T17:45:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80"
    ],
    "keywords": [
      "reduction modulo",
      "strongly divisible modules",
      "absolute galois group",
      "galois stable lattices",
      "dimensional semi-stable representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2362P"
    }
  }
}