2002/03/21 by Janós Kollár, János Kollár, Kollár, János +2 · 1 citation
Computer Science · Mathematics · #14G15 #14G20 (secondary) #14J20 #14M20 (primary) 14C15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #math.AG #msc:14C15 #msc:14G15 #msc:14G20 #msc:14J20 #msc:14M20
paper · pdf · doi:10.48550/arxiv.math/0203220
openalex publication_date 2002/03/21 · arxiv created 2002/12/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.