Specialization of zero cycles

Details Specialization of zero cycles Specialization of zero cycles

2002-05-14

arxiv.org/abs/math/0205148v1

Mathematics

Algebraic Geometry

Scientific paper

The paper has two parts. First we prove that the specialization maps on R-equivalence and on the Chow group of zero cycles are isomorphisms for families over a local, Henselian, Dedekind ring when the special fiber is smooth and separably rationally connected. This is pretty much the best one can hope for. The second part contains examples of unirational quartic hypersurfaces whith infinitely many R-equivalence classes. There are also examples of quartics with points in a large odd degree field extension but no points in any smaller odd degree extension.

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