{
  "id": "math/0304202",
  "version": "v1",
  "published": "2003-04-15T21:20:29.000Z",
  "updated": "2003-04-15T21:20:29.000Z",
  "title": "The first two cohomology groups of some Galois groups",
  "authors": [
    "Jan Minac",
    "Adrian Wadsworth"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo $p^n$th powers of a related field, and we obtain transparent proofs and slight generalizations of some classical results of Albert. The potential application to the cyclicity question for division algebras of degree $p$ is outlined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-15T21:20:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois groups",
      "residue classes modulo",
      "galois cohomology groups",
      "th powers",
      "th root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4202M"
    }
  }
}