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1 November 2003 Rationally connected varieties over finite fields
János Kollár, Endre Szabó
Duke Math. J. 120(2): 251-267 (1 November 2003). DOI: 10.1215/S0012-7094-03-12022-0

Abstract

Let $X$ be a geometrically rational (or, more generally, separably rationally connected) variety over a finite field $K$. We prove that if $K$ is large enough, then $X$ contains many rational curves defined over $K$. As a consequence we prove that $R$-equivalence is trivial on $X$ if $K$ is large enough. These results imply the following conjecture of J.-L. Colliot-Thélène: Let $Y$ be a rationally connected variety over a number field $F$. For a prime $P$, let $Y_P$ denote the corresponding variety over the local field $F_P$. Then, for almost all primes $P$, the Chow group of 0-cycles on $Y_P$ is trivial and $R$-equivalence is trivial on $Y_P$.

Citation

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János Kollár. Endre Szabó. "Rationally connected varieties over finite fields." Duke Math. J. 120 (2) 251 - 267, 1 November 2003. https://doi.org/10.1215/S0012-7094-03-12022-0

Information

Published: 1 November 2003
First available in Project Euclid: 16 April 2004

zbMATH: 1077.14068
MathSciNet: MR2019976
Digital Object Identifier: 10.1215/S0012-7094-03-12022-0

Subjects:
Primary: 14G15, 14J20, 14M20
Secondary: 14C15, 14G20

Rights: Copyright © 2003 Duke University Press

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Vol.120 • No. 2 • 1 November 2003
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