A generalized etale cohomology idea is a conception that is represented via a presheaf of spectra on an etale website for an algebraic kind, in analogy with the way in which a standard spectrum represents a cohomology thought for areas. Examples contain etale cohomology and etale K-theory. This e-book provides 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 lots of the significant rules of the homotopy thought 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 sturdy homotopy concept for n-fold spectra, that's then promoted to the extent of presheaves of n-fold spectra.
This e-book might be of curiosity to all researchers operating in fields with regards to algebraic K-theory. The suggestions provided listed below are primarily combinatorial, and consequently algebraic. an intensive heritage in conventional sturdy homotopy idea isn't assumed.
(...) in constructing the recommendations of the topic, introduces the reader to the sturdy homotopy class of simplicial presheaves. (...) This publication offers the person with the 1st whole account that is delicate sufficient to be appropriate with this sort of closed version classification beneficial in K-theory functions (...). As an software of the strategies the writer offers 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 no Bott periodicity). the hot facts of this conjecture, by means of V. Voevodsky, (...) makes this quantity obligatory interpreting for all who are looking to be au fait with present traits in algebraic K-theory!
- Zentralblatt MATH
The presentation of those issues is very unique. The publication could be very valuable for any researcher drawn to matters relating to algebraic K-theory.
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