{
  "id": "1704.05713",
  "version": "v1",
  "published": "2017-04-19T12:56:50.000Z",
  "updated": "2017-04-19T12:56:50.000Z",
  "title": "Finite Generation of Extensions of Associated Graded Rings Along a Valuation",
  "authors": [
    "Steven Dale Cutkosky"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "In this paper we consider the question of when the associated graded ring along a valuation, ${\\rm gr}_{\\nu^*}(S)$, is a finite ${\\rm gr}_{\\nu^*}(R)$-module, where $S$ is a normal local ring which lies over a normal local ring $R$ and $\\nu^*$ is a valuation of the quotient field of $S$ which dominates $S$. We obtain a very general result in equicharacteristic zero in Theorem 1.5. We also obtain general results for unramified extensions of excellent local rings in Proposition 1.7.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-19T12:56:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14B22",
      "13B10",
      "11S15"
    ],
    "keywords": [
      "associated graded ring",
      "finite generation",
      "extensions",
      "normal local ring",
      "general result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}