{
  "id": "1007.0332",
  "version": "v1",
  "published": "2010-07-02T10:37:37.000Z",
  "updated": "2010-07-02T10:37:37.000Z",
  "title": "Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different",
  "authors": [
    "Erik Jarl Pickett"
  ],
  "journal": "Journal of Number Theory, Volume 129, Issue 7, July 2009, Pages 1773-1785",
  "doi": "10.1016/j.jnt.2009.02.012",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a finite extension of $\\Q_p$, let $L/K$ be a finite abelian Galois extension of odd degree and let $\\bo_L$ be the valuation ring of $L$. We define $A_{L/K}$ to be the unique fractional $\\bo_L$-ideal with square equal to the inverse different of $L/K$. For $p$ an odd prime and $L/\\Q_p$ contained in certain cyclotomic extensions, Erez has described integral normal bases for $A_{L/\\Q_p}$ that are self-dual with respect to the trace form. Assuming $K/\\Q_p$ to be unramified we generate odd abelian weakly ramified extensions of $K$ using Lubin-Tate formal groups. We then use Dwork's exponential power series to explicitly construct self-dual integral normal bases for the square-root of the inverse different in these extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-02T10:37:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit construction",
      "abelian weakly ramified extensions",
      "square-root",
      "odd abelian",
      "construct self-dual integral normal bases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0332J"
    }
  }
}