Rationality of Integral Cycles

  • Alexander Vishik

    School of Mathematical Sciences University of Nottingham University Park Nottingham NG7 2RD, United Kingdom


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 Z/2\Bbb Z/2-coefficients. We also show that modulo 2 and degree rr cohomological invariants of algebraic varieties can not affect rationality of cycles of codimensions up to 2r122^{r-1}-2.