{
  "id": "1107.1634",
  "version": "v2",
  "published": "2011-07-08T13:51:18.000Z",
  "updated": "2011-12-06T19:13:15.000Z",
  "title": "Arithmetic of 0-cycles on varieties defined over number fields",
  "authors": [
    "Yongqi Liang"
  ],
  "comment": "21 pages, part of the main result appeared in an old version of the author's preprint (arXiv:1011.5995), the proof here is simplified",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $X$ be a rationally connected algebraic variety, defined over a number field $k$. We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for $K$-rational points on $X_K$ for all finite extensions $K/k$; (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree 1 on $X_K$ for all finite extensions $K/k$; (3) a certain sequence of local-global type for Chow groups of 0-cycles on $X_K$ is exact for all finite extensions $K/k$. We prove that (1) implies (2), and that (2) and (3) are equivalent. We also prove a similar implication for the Hasse principle. As an application, we prove the exactness of the sequence mentioned above for smooth compactifications of certain homogeneous spaces of linear algebraic groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-06T19:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G25",
      "11G35",
      "14M22"
    ],
    "keywords": [
      "number field",
      "finite extensions",
      "arithmetic",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1634L"
    }
  }
}