### Abstract

Let k be a function field in one variable over C or the field C((t)). Let X be a k-rationally simply connected variety defined over k. In this paper we show that R-equivalence on rational points of X is trivial and that the Chow group of zero-cycles of degree zero A _{0}(X) is zero. In particular, this holds for a smooth complete intersection of r hypersurfaces in P _{k} ^{n} of respective degrees (equation required).

Original language | English (US) |
---|---|

Pages (from-to) | 707-719 |

Number of pages | 13 |

Journal | Journal of Algebraic Geometry |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - 2012 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

**R-equivalence on low degree complete intersections.** / Pirutka, Alena.

Research output: Contribution to journal › Article

*Journal of Algebraic Geometry*, vol. 21, no. 4, pp. 707-719. https://doi.org/10.1090/S1056-3911-2011-00581-X

}

TY - JOUR

T1 - R-equivalence on low degree complete intersections

AU - Pirutka, Alena

PY - 2012

Y1 - 2012

N2 - Let k be a function field in one variable over C or the field C((t)). Let X be a k-rationally simply connected variety defined over k. In this paper we show that R-equivalence on rational points of X is trivial and that the Chow group of zero-cycles of degree zero A 0(X) is zero. In particular, this holds for a smooth complete intersection of r hypersurfaces in P k n of respective degrees (equation required).

AB - Let k be a function field in one variable over C or the field C((t)). Let X be a k-rationally simply connected variety defined over k. In this paper we show that R-equivalence on rational points of X is trivial and that the Chow group of zero-cycles of degree zero A 0(X) is zero. In particular, this holds for a smooth complete intersection of r hypersurfaces in P k n of respective degrees (equation required).

UR - http://www.scopus.com/inward/record.url?scp=84867644553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867644553&partnerID=8YFLogxK

U2 - 10.1090/S1056-3911-2011-00581-X

DO - 10.1090/S1056-3911-2011-00581-X

M3 - Article

VL - 21

SP - 707

EP - 719

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

SN - 1056-3911

IS - 4

ER -