{
  "id": "math/0405503",
  "version": "v5",
  "published": "2004-05-26T16:23:47.000Z",
  "updated": "2007-09-07T15:07:34.000Z",
  "title": "Galois module structure of Milnor K-theory in characteristic p",
  "authors": [
    "Ganesh Bhandari",
    "Nicole Lemire",
    "Jan Minac",
    "John Swallow"
  ],
  "comment": "v5 (10 pages); revised introduction and shortened paper; incorporated and acknowledged suggestions by readers of earlier versions",
  "journal": "New York J. Math. 14 (2008), 215--224",
  "categories": [
    "math.NT",
    "math.KT",
    "math.RT"
  ],
  "abstract": "Let E be a cyclic extension of degree p^n of a field F of characteristic p. Using arithmetic invariants of E/F we determine k_mE, the Milnor K-groups K_mE modulo p, as Fp[Gal(E/F)]-modules for all m in N. In particular, we show that each indecomposable summand of k_mE has Fp-dimension a power of p. That all powers p^i, i=0,1,...,n, occur for suitable examples is shown in a subsequent paper [MSS2], where additionally the main result of this paper becomes an essential induction step in the determination of K_mE/p^sK_mE as (Z/p^sZ)[Gal(E/F)]-modules for all m, s in N.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-09-07T15:07:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19D45",
      "12F10"
    ],
    "keywords": [
      "galois module structure",
      "milnor k-theory",
      "characteristic",
      "essential induction step",
      "milnor k-groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5503B"
    }
  }
}