ENGLISH

Generalized Etale Cohomology Theories

By J. F. Jardine

Book information

Publisher
Birkhauser Verlag
Year
1997
ISBN
9780817654948, 0-8176-5494-1, 3764354941
LCC
QA564 .J34 1997
Open Library ID
OL1011731M
Language
english
Format
DJVU
Filesize
6 MB (6714214 bytes)
Series
Progress in mathematics 146
Pages
163\163
Topic
Mathematics Algebra
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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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