Generalized Etale Cohomology Theories (Progress in Mathematics)

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9783764354947: Generalized Etale Cohomology Theories (Progress in Mathematics)

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed.

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About the Author:

John F. Jardine is a Professor of mathematics at the University of Western Ontario, Canada.

Review:

"This book provides the user with the first complete account which is sensitive enough to be compatible with the sort of closed model category necessary in K-theory applications... Compulsory reading for all who want to be au fait with current trends in algebraic K-theory!"

--Mathematical Reviews

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J.F. Jardine
Published by Birkhäuser (2004)
ISBN 10: 3764354941 ISBN 13: 9783764354947
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