## Rationality of integral cycles

### Summary

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 $\Bbb Z/2$-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 $2^{r-1}-2$.

### Mathematics Subject Classification

14C15, 11E04, 14C25, 19D45, 55S25

### Keywords/Phrases

quadric, function field of a quadric, Chow group, algebraic cobordism, symmetric operation, Landweber-Novikov operation, rationality