- Based upon lectures given by V. Voevodsky in 1999-2000

- Carlo Mazza, Vladimir Voevodsky and Charles Weibel

Here are the Lectures on Motivic Cohomology (it is a 230-page pdf file, 1.0 MB, December 2005) This is the final version of the notes.

It has been published in 2006 by the AMS as volume 2 of the

It begins with a Table of Contents, including a Dependency Chart, and contains an index and a glossary.

During the academic year 1999-2000, Voevodsky gave a course on motivic cohomology at the Institute for Advanced Study in Princeton. These lecture notes reflect the content of this course. They may be divided into two terms. The Fall term (Lectures 1-10) contains the basic definitions, organized around the notion of a presheaf with transfers, together with the fundamental comparisons with other known invariants: Picard group, Milnor K-theory and etale cohomology.

The Spring Term centers around Nisnevich sheaves with transfer.
Lectures 11-14 contains the construction of the triangulated category
of motives over a field, **DM**. The key technical result, that
the cohomology of a homotopy invariant Nisnevich sheaf with transfers
is homotopy invariant, is postponed to Lectures 21-24. Lectures 16-19
establish the isomorphism between motivic cohomology and higher Chow
groups, without assuming resolution of singularities. Other properties
of **DM** are developed in Lectures 14, 16 and 20.

This site maintained by Charles Weibel / weibel @ math.rutgers.edu/ August 28, 2008