{
  "id": "1305.2580",
  "version": "v4",
  "published": "2013-05-12T12:38:34.000Z",
  "updated": "2016-01-13T08:11:34.000Z",
  "title": "Tame ramification and group cohomology",
  "authors": [
    "Chandan Singh Dalawat",
    "Jung-Jo Lee"
  ],
  "comment": "Cleaner version, 24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give an intrinsic parametrisation of the set of tamely ramified extensions of a local field with finite residue field and bring to the fore the role played by group cohomology. We show that two natural definitions of the cohomology class of a tamely ramified finite galoisian extension coincide, and can be recovered from the parameter. We also give an elementary proof of Serre's mass formula in the tame case and in the simplest wild case, and we classify tame galoisian extensions of degree the cube of a prime.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-21T11:05:01.000Z",
      "abstract": "We give an intrinsic parametrisation of the set of tamely ramified extensions $L$ (of given ramification index $e$ and residual degree $f$) of a local field $K$ with finite residue field of characteristic $p$. We show that when $L|K$ is galoisian, two natural definitions of the cohomology class of $L|K$ coincide (and can be recovered from the parameter), give an elementary proof of Serre's mass formula over $K$ in the tame case (and in the simplest wild case) and classify galoisian extensions $L|K$ of degree $l^3$ ($l$ being a prime $\\neq p$).",
      "comment": "abridged version, 19 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-01-13T08:11:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S15",
      "11S20"
    ],
    "keywords": [
      "group cohomology",
      "tame ramification",
      "simplest wild case",
      "serres mass formula",
      "finite residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2580S"
    }
  }
}