عنوان

Generalized étale cohomology theories /

(Number (ISBN

3034800665

(Number (ISBN

9783034800662

Erroneous ISBN

0817654941

Erroneous ISBN

3034800657

Erroneous ISBN

3764354941

Erroneous ISBN

9780817654948

Erroneous ISBN

9783034800655

Erroneous ISBN

9783764354947

Number

b737202

Title Proper

Generalized étale cohomology theories /

General Material Designation

[Book]

First Statement of Responsibility

J.F. Jardine.

Place of Publication, Distribution, etc.

Basel :

Name of Publisher, Distributor, etc.

Birkhäuser,

Date of Publication, Distribution, etc.

[2010]

Date of Publication, Distribution, etc.

©1997

Specific Material Designation and Extent of Item

1 online resource (x, 317 pages) :

Other Physical Details

illustrations

Series Title

Modern Birkhäuser classics

Text of Note

Originally published 1997 as v. 146 of Progress in mathematics (Boston, Mass.).

Text of Note

Reprinted 2010 by Springer Basel.

Text of Note

Includes bibliographical references (pages 313-315) and index.

Text of Note

Smash products of spectra -- Abstract homotopy theory of n-fold spectra -- First applications -- Auxilliary results -- K-theory presheaves -- Generalized tale cohomology -- Bott periodic K-theory.

0

Text of 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 Thomasons 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.

Title

Generalized étale cohomology theories

International Standard Book Number

9783034800655

Geometry, Algebraic.

Homology theory.

Geometry, Algebraic.

Homology theory.

Number

Edition

Class number

Book number

Jardine, J. F.,1951-

Date of Transaction

20201203220037.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y