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Field name	Details
Dewey Class	510
Title	Generalized Etale Cohomology Theories ([EBook] /) / by John F. Jardine.
Author	Jardine, John F.
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Springer Basel, , 1997.
Physical Details	X, 317 p. : online resource.
Series	Modern Birkhäuser classics
ISBN	9783034800662
Summary Note	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. ------ Reviews (…) in developing the techniques of the subject, introduces the reader to the stable homotopy category of simplicial presheaves. (…) 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 (…). As an application of the techniques the author gives proofs of the descent theorems of R. W. Thomason and Y. A. Nisnevich. (…) The book concludes with a discussion of the Lichtenbaum-Quillen conjecture (an approximation to Thomason’s theorem without Bott periodicity). The recent proof of this conjecture, by V. Voevodsky, (…) makes this volume compulsory reading for all who want to be au fait with current trends in algebraic K-theory! - Zentralblatt MATH The presentation of these topics is highly original. The book will be very useful for any researcher interested in subjects related to algebraic K-theory. - Matematica.:
Contents note	Smash products of spectra -- Abstract homotopy theory of n-fold spectra -- First applications -- Auxilliary results -- K-theory presheaves -- Generalized étale cohomology -- Bott periodic K-theory.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0066-2
Links to Related Works	Subject References: Mathematics . Mathematics, general . Authors: Jardine, John F. . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 510 .

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Generalized Etale Cohomology Theories

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