Author: Vladimir Voevodsky
Title: Motivic cohomology are isomorphic to higher Chow groups
Email: vladimir@math.ias.edu

In this short paper we show that the motivic cohomology groups defined
in "Cycles, transfers and motivic homology theories" (No. 368 of this
archive) are isomorphic to the higher Chow groups for smooth varieties
over any field. Because of the homotopy invariance property of higher
Chow groups this implies that the Cancellation Theorem holds over any
field. Both facts were previously known only under the resolution of
singularities assumption.