{
  "id": "1708.05382",
  "version": "v1",
  "published": "2017-08-17T17:56:42.000Z",
  "updated": "2017-08-17T17:56:42.000Z",
  "title": "Bass and Schur finiteness conjectures for quadric fibrations",
  "authors": [
    "Goncalo Tabuada"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.KT",
    "math.RT"
  ],
  "abstract": "Let q: Q-->B be a quadric fibration. Making use of the recent theory of noncommutative motives, we establish a precise relation between the Bass and Schur finiteness conjectures for Q and the Bass and Schur finiteness conjectures for certain coverings/subschemes of B. As an application, we prove the Bass and Schur finiteness conjectures for Q whenever B is low-dimensional. As a byproduct, we obtain a proof of the Bass and Schur finiteness conjectures for smooth complete intersections of two or three quadric hypersurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-17T17:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A20",
      "14A22",
      "14C15",
      "14M10",
      "19E08"
    ],
    "keywords": [
      "schur finiteness conjectures",
      "quadric fibration",
      "smooth complete intersections",
      "precise relation",
      "quadric hypersurfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}