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  Journal of Algebraic Geometry
Journal of Algebraic Geometry
Online ISSN 1534-7486; Print ISSN 1056-3911



$ R$-equivalence on low degree complete intersections

Author: Alena Pirutka
Journal: J. Algebraic Geom. 21 (2012), 707-719
Published electronically: November 9, 2011
MathSciNet review: 2957693
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Abstract: Let $ k$ be a function field in one variable over $ \mathbb{C}$ or the field $ \mathbb{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 $ \mathbb{P}^n_k$ of respective degrees $ d_1,\ldots ,d_r$ with $ \sum \limits _{i=1}^{r}d_i^2\leq n+1$.

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Additional Information

Alena Pirutka
Affiliation: École Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France

PII: S 1056-3911(2011)00581-X
Received by editor(s): December 4, 2009
Received by editor(s) in revised form: November 23, 2010
Published electronically: November 9, 2011

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
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Online ISSN 1534-7486; Print ISSN 1056-3911
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