{
  "id": "2108.13594",
  "version": "v1",
  "published": "2021-08-31T02:56:23.000Z",
  "updated": "2021-08-31T02:56:23.000Z",
  "title": "On extension of the motivic cohomology beyond smooth schemes",
  "authors": [
    "Jinhyun Park"
  ],
  "comment": "106 pages",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on the category, that it detects nilpotence, and that its restriction to the subcategory of smooth schemes agrees with the pre-existing motivic cohomology theory, which is the higher Chow theory of S. Bloch (Adv. Math., 1986). A few structures and applications are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-31T02:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14B20",
      "14F42",
      "14A30",
      "19E15",
      "16W60",
      "18F20"
    ],
    "keywords": [
      "smooth schemes",
      "higher chow theory",
      "pre-existing motivic cohomology theory",
      "admit arbitrary singularities",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 106,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}