The Norm Residue Isomorphism Theorem , by Charles A. Weibel

This is an expanded version of the preprint /K-theory/0844, "Patching the Norm Residue Isomorphism Theorem" (the word 'Patching' has been removed from the title). It will appear in the Journal of Topology.

Two new sections have been added. Section 2 (Motivic Model Structures) explains the passage between the various homotopy categories in terms of Quillen adjunctions, which is used to construct classifying spaces. Section 7 (χ Duality) is an exposition of the notion of duality for motives over the embedded scheme χ and is used in the definition of a Rost motive.

I would like to thank the referee for asking that this material be included.

Charles A. Weibel < >