TY - JOUR

T1 - Rationally connected varieties over finite fields

AU - Kollár, János

AU - Szabó, Endre

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2003/11/1

Y1 - 2003/11/1

N2 - 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 YP denote the corresponding variety over the local field FP. Then, for almost all primes P, the Chow group of 0-cycles on YP is trivial and R-equivalence is trivial on YP.

AB - 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 YP denote the corresponding variety over the local field FP. Then, for almost all primes P, the Chow group of 0-cycles on YP is trivial and R-equivalence is trivial on YP.

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U2 - 10.1215/S0012-7094-03-12022-0

DO - 10.1215/S0012-7094-03-12022-0

M3 - Article

AN - SCOPUS:0347651599

VL - 120

SP - 251

EP - 267

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 2

ER -