{
  "id": "1803.01463",
  "version": "v1",
  "published": "2018-03-05T02:37:48.000Z",
  "updated": "2018-03-05T02:37:48.000Z",
  "title": "Motivic cohomology of fat points in Milnor range",
  "authors": [
    "Jinhyun Park",
    "Sinan Ünver"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials $k[t]/(t^m)$ in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We compute the groups in the Milnor range when the base field is of characteristic $0$, and prove that they give the Milnor $K$-groups of $k[t]/(t^m)$, whose relative part is the sum of the absolute K\\\"ahler differential forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T02:37:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25"
    ],
    "keywords": [
      "milnor range",
      "fat points",
      "motivic cohomology theory",
      "algebraic-cycle model",
      "deformation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}