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Generalized Etale Cohomology Theories

✍ Scribed by J. F. Jardine

Book ID
127446434
Publisher
Birkhäuser Verlag
Year
1997
Tongue
English
Weight
6 MB
Series
Progress in mathematics 146
Category
Library
City
Basel; Boston
ISBN-13
9783764354947

No coin nor oath required. For personal study only.

✦ 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 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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