Products in Higher Chow groups and Motivic Cohomology, by Charles Weibel

We prove a compatibility theorem for the various products which have been defined on several cohomology theories. If X is smooth over a field which admits resolution of singularities, then it is known that Bloch's higher Chow groups of X, the Friedlander--Voevodsky bivariant cycle cohomology of X and Voevodsky's motivic cohomology of X coincide. We prove that these isomorphisms identify the product structures. We also prove that the map to etale cohomology is compatible with products.

This paper appeared in Proc. Symp. Pure Math. 67 (1999), 305-315.

Charles Weibel <>