Rationality of Integral Cycles

In this article we provide the sufficient condition for a Chow group element to be defined over the ground field. This is an integral version of the result known for $\zz/2$-coefficients. We also show that modulo 2 and degree $r$ cohomological invariants of algebraic varieties can not affect rationality of cycles of codimensions up to $2^{r-1}-2$.

2010 Mathematics Subject Classification: 11E04, 14C15, 14C25, 19D45, 55S25

Keywords and Phrases: Quadrics, Chow groups, algebraic cobordism, Landweber-Novikov operations, Symmetric operations

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