Lectures on Motivic Cohomology, by Vladimir Voevodsky, Carlo Mazza, and Charles Weibel

May 20, 2005: The book has been revised and upgraded. Hopefully this is the final version.

This book is based on the lectures on motivic cohomology which Voevodsky gave at the Institute for Advance Study in Princeton during 1999/2000. Although we still anticipate making small changes, the "beta" version of the notes is now available at the following web site.

The first half of the text was originally made available in May 2001, and corresponds to the fall term of 1999. The first half of the present version differs from the 2001 version in some respects, such as the addition of appendix 8A on "Tensor Triangulated Categories."

The idea of these lectures was to define motivic cohomology and to give careful proofs of the elementary results which relate it to other known invariants of algebraic varieties. In the process, we need to develop many of the main structural properties of motivic cohomology. As a result, these lectures cover a considerable portion of the book "Cycles, Transfers and Motivic Homology Theories", but from a different point of view.

Vladimir Voevodsky <vladimir@math.ias.edu>
Carlo Mazza <mazzac@math.rutgers.edu>
Charles Weibel <weibel@math.rutgers.edu>