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 $H^3(F,\mathbf{Q}/\mathbf{Z}(2))\to H^3(F(X),\mathbf{Q}/\mathbf{Z}(2))$ to the torsion of $C{H}^{2}X$ for rational varieties $X$.