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Rationally connected varieties over finite fields

János Kollár·Endre Szabó
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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 imply that if Y is defined over a local field and it has good, separably rationally connected reduction then the Chow group of zero cycles is trivial for any residue field. R-equivalence is also trivial if the residue field is large enough.

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János Kollár, Endre Szabó. 2002-12-02. Rationally connected varieties over finite fields. https://arxiv.org/abs/math/0203220

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