{
  "id": "1709.10259",
  "version": "v1",
  "published": "2017-09-29T07:23:12.000Z",
  "updated": "2017-09-29T07:23:12.000Z",
  "title": "On complete intersections in varieties with finite-dimensional motive",
  "authors": [
    "Robert Laterveer",
    "Jan Nagel",
    "Chris Peters"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a complete intersection inside a variety $M$ with finite dimensional motive and for which the Lefschetz-type conjecture $B(M)$ holds. We show how conditions on the niveau filtration on the homology of $X$ influence directly the niveau on the level of Chow groups. This leads to a generalization of Voisin's result. The latter states that if $M$ has trivial Chow groups and if $X$ has non-trivial variable cohomology parametrized by $c$-dimensional algebraic cycles, then the cycle class maps $A_k(X) \\to H_{2k}(X)$ are injective for $k<c$. We give variants involving group actions which lead to several new examples with finite dimensional Chow motives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-29T07:23:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30"
    ],
    "keywords": [
      "finite-dimensional motive",
      "finite dimensional chow motives",
      "complete intersection inside",
      "cycle class maps",
      "trivial chow groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}