R-equivalence on low degree complete intersections

Details R-equivalence on low degree complete intersections R-equivalence on low degree complete intersections

2009-07-11

arxiv.org/abs/0907.1971v2

Mathematics

Algebraic Geometry

11 pages

Scientific paper

Let $k$ be the function field of a complex curve or the field $C((t))$. We
show that for a smooth complete intersection $X$ of $r$ hypersurfaces in
$P^n_k$ of respective degrees $d_1,...,d_r$ with $\sum d_i^2\leq n+1$ the
R-equivalence on rational points of $X$ is trivial and the Chow group of
zero-cycles of degree zero $A_0(X)$ is zero.

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