``Lectures in Motivic Cohomology''

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 Clay Monographs in Math series.

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.

Known Errata

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