{
  "id": "math/0701861",
  "version": "v1",
  "published": "2007-01-29T20:16:44.000Z",
  "updated": "2007-01-29T20:16:44.000Z",
  "title": "Algebraic cycles on Severi-Brauer schemes of prime degree over a curve",
  "authors": [
    "Cristian D. Gonzalez-Aviles"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $k$ be a perfect field and let $p$ be a prime number different from the characteristic of $k$. Let $C$ be a smooth, projective and geometrically integral $k$-curve and let $X$ be a Severi-Brauer $C$-scheme of relative dimension $p-1$ . In this paper we show that $CH^{d}(X)_{{\\rm{tors}}}$ contains a subgroup isomorphic to $CH_{0}(X/C)$ for every $d$ in the range $2\\leq d\\leq p$. We deduce that, if $k$ is a number field, then $CH^{d}(X)$ is finitely generated for every $d$ in the indicated range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-29T20:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14C15"
    ],
    "keywords": [
      "severi-brauer schemes",
      "prime degree",
      "algebraic cycles",
      "perfect field",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1861G"
    }
  }
}