Applications of weight-two motivic cohomology

Abstract

Using Lichtenbaum's complex $\Gamma(2)$, we reprove and extend a little bit some known results relating the kernel of $H^3(F,{\bold Q}/{\bold Z}(2))\to H^3(F(X),{\bold Q}/{\bold Z}(2))$ to the torsion of $CH^2 X$ for rational varieties $X$.