A generalized etale cohomology concept is a concept that is represented by way of a presheaf of spectra on an etale website for an algebraic sort, in analogy with the way in which a standard spectrum represents a cohomology thought for areas. Examples comprise etale cohomology and etale K-theory. This e-book offers new and entire proofs of either Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes many of the significant principles of the homotopy idea of presheaves of spectra, and generalized etale homology theories particularly. The remedy comprises, for the aim of properly facing cup product buildings, a improvement of reliable homotopy thought for n-fold spectra, that's then promoted to the extent of presheaves of n-fold spectra.
This e-book will be of curiosity to all researchers operating in fields with regards to algebraic K-theory. The ideas offered listed here are basically combinatorial, and for this reason algebraic. an in depth historical past in conventional reliable homotopy idea isn't assumed.
(...) in constructing the concepts of the topic, introduces the reader to the solid homotopy type of simplicial presheaves. (...) This ebook presents the consumer with the 1st whole account that is delicate sufficient to be suitable with this kind of closed version type invaluable in K-theory functions (...). As an program of the strategies the writer supplies proofs of the descent theorems of R. W. Thomason and Y. A. Nisnevich. (...) The e-book concludes with a dialogue of the Lichtenbaum-Quillen conjecture (an approximation to Thomason's theorem with out Bott periodicity). the new facts of this conjecture, through V. Voevodsky, (...) makes this quantity obligatory examining for all who are looking to be au fait with present developments in algebraic K-theory!
- Zentralblatt MATH
The presentation of those issues is very unique. The booklet might be very worthwhile for any researcher attracted to topics concerning algebraic K-theory.
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