Rationally connected varieties over finite fields

János Kollár, Endre Szabó

Research output: Contribution to journalArticle

16 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)251-267
Number of pages17
JournalDuke Mathematical Journal
Volume120
Issue number2
DOIs
StatePublished - Nov 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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