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
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Series: |
Modern Birkhauser Classics |
Release date: |
December 2010 |
First published: |
1997 |
Authors: |
John F. Jardine
|
Dimensions: |
235 x 155 x 17mm (L x W x T) |
Format: |
Paperback
|
Pages: |
317 |
Edition: |
Reprint of the 1997 Edition |
ISBN-13: |
978-3-03-480065-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
Algebraic topology
|
LSN: |
3-03-480065-7 |
Barcode: |
9783034800655 |
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