{
  "id": "1604.06155",
  "version": "v1",
  "published": "2016-04-21T01:47:38.000Z",
  "updated": "2016-04-21T01:47:38.000Z",
  "title": "Cube invariance of higher Chow groups with modulus",
  "authors": [
    "Hiroyasu Miyazaki"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AG",
    "math.KT",
    "math.NT"
  ],
  "abstract": "We introduce a generalized notion of higher Chow groups with modulus. We generalize $\\mathbb{A}^1$-homotopy invariance of Bloch's higher Chow groups to an invariance property of higher Chow groups with modulus, called cube-invariance. For the proof of cube-invariance, we need a moving lemma of algebraic cycles which takes modulus conditions into account. As an application of cube-invariance, we prove that over a field of positive characteristic $p$, the higher Chow group with modulus, after $p$ inverted, is $\\mathbb{A}^1$-homotopy invariant and is independent of the multiplicity of modulus divisors. We can obtain a similar independence result on relative motivic cohomology groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-21T01:47:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14C15",
      "14F42",
      "14F43"
    ],
    "keywords": [
      "cube invariance",
      "blochs higher chow groups",
      "similar independence result",
      "cube-invariance",
      "relative motivic cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160406155M"
    }
  }
}