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Other titles in the Modern Birkhauser Classics series:
Generalized Etale Cohomology Theories (Modern Birkhauser Classics)by John F. Jardine
Synopses & ReviewsPublisher Comments: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 Ktheory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic Ktheory 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 nfold spectra, which is then promoted to the level of presheaves of nfold spectra. This book should be of interest to all researchers working in fields related to algebraic Ktheory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed. 
Synopsis:This book offers new, complete proofs of both Thomason's descent theorem for Bott periodic Ktheory and the Nisnevich descent theorem, exposing major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular.
Synopsis: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 Ktheory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic Ktheory 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 nfold spectra, which is then promoted to the level of presheaves of nfold spectra. This book should be of interest to all researchers working in fields related to algebraic Ktheory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed.
About the AuthorJohn F. Jardine is a Professor of mathematics at the University of Western Ontario, Canada.
Table of ContentsChapter 1. Smash products of spectra Chapter 2. Abstract homotopy theory of nfold spectra Chapter 3. First applications Chapter 4. Auxilliary results Chapter 5. Ktheory presheaves Chapter 6. Generalized étale cohomology Chapter 7. Bott periodic Ktheory References Index
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Related SubjectsScience and Mathematics » Mathematics » General Science and Mathematics » Mathematics » Topology 

