{
  "id": "1906.08232",
  "version": "v1",
  "published": "2019-06-19T17:27:07.000Z",
  "updated": "2019-06-19T17:27:07.000Z",
  "title": "Representability of Chow groups of codimension three cycles",
  "authors": [
    "Kalyan Banerjee"
  ],
  "comment": "10 pages, comments are welcome",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "In this note we are going to prove that if we have a fibration of smooth projective varieties $X\\to S$ over a surface $S$ such that $X$ is of dimension four and that the geometric generic fiber has finite dimensional motive and the first \\'etale cohomology of the geometric generic fiber with respect to $\\QQ_l$ coefficients is zero and the second \\'etale cohomology is spanned by divisors, then $A^3(X)$ (codimension three algebraically trivial cycles modulo rational equivalence) is dominated by finitely many copies of $A_0(S)$. Meaning that there exists finitely many correspondences $\\Gamma_i$ on $S\\times X$, such that $\\sum_i \\Gamma_i$ is surjective from $\\oplus A^2(S)$ to $A^3(X)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-19T17:27:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25"
    ],
    "keywords": [
      "chow groups",
      "geometric generic fiber",
      "codimension",
      "trivial cycles modulo rational equivalence",
      "representability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}