Generalized Étale Cohomology Theories, by J. F. Jardine

A generalized étale cohomology theory is a cohomology theory which is represented by a presheaf of spectra on some étale site. Étale K-theory is the most prominent example.

This monograph gives modern proofs of Thomason's étale cohomological descent theorem for Bott periodic K-theory and the Nisnevich descent theorem, and discusses the portions of the homotopy theory of presheaves of spectra which are necessary to effect these proofs. The presheaf-theoretic approach to the Lichtenbaum-Quillen conjecture is also discussed.

Other items of particular interest appearing here include an elementary description of the theory of smash products of presheaves of spectra, and a thorough discussion of generalized Galois cohomology theories arising from the homotopy theory of presheaves of spectra on the site of finite discrete G-sets for an arbitrary profinite group G.

This book is scheduled to appear some time in February, 1997. Here's the reference:

J.F. Jardine, Generalized Étale Cohomology Theories, Progress in Math., Vol. 146, Birkhauser, Boston-Basel-Berlin, 1997.

The files for the book have been removed from this server. They comprised a version of the manuscript that was completed in late 1993; the published version has been substantially revised.

J. F. Jardine <>