{
  "id": "1903.11541",
  "version": "v1",
  "published": "2019-03-27T16:48:41.000Z",
  "updated": "2019-03-27T16:48:41.000Z",
  "title": "Regulator Maps for Higher Chow Groups via Current Transforms",
  "authors": [
    "Pedro F. dos Santos",
    "Robert M. Hardt",
    "Paulo Lima-Filho"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We show how to use equidimensional algebraic correspondences between complex algebraic varieties to construct pull-backs and transforms of certain classes of geometric currents. Using this construction we produce explicit formulas at the level of complexes for a regulator map from the Higher Chow groups of smooth complex quasi-projective algebraic varieties to Deligne-Beilinson cohomology with integral coefficients. A distinct aspect of our approach is the use of Suslin's complex of equidimensional cycles over $ \\Delta^n $ to compute Bloch's higher Chow groups. We calculate explicit examples involving the M\\\"{a}hler measure of Laurent polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-27T16:48:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14C30",
      "14C35",
      "19E15",
      "32C30"
    ],
    "keywords": [
      "regulator map",
      "current transforms",
      "blochs higher chow groups",
      "smooth complex quasi-projective algebraic varieties",
      "produce explicit formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}