Coverart for item
The Resource Étale cohomology, J.S. Milne

Étale cohomology, J.S. Milne

Label
Étale cohomology
Title
Étale cohomology
Statement of responsibility
J.S. Milne
Creator
Author
Subject
Genre
Language
eng
Summary
One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series
Member of
Cataloging source
N$T
http://library.link/vocab/creatorDate
1942-
http://library.link/vocab/creatorName
Milne, J. S.
Illustrations
illustrations
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Princeton mathematical series
Series volume
33
http://library.link/vocab/subjectName
  • Geometry, Algebraic
  • Homology theory
  • Sheaf theory
  • Géométrie algébrique
  • Homologie
  • Faisceaux, Théorie des
  • MATHEMATICS
  • Geometry, Algebraic
  • Homology theory
  • Sheaf theory
  • Cohomologie
  • Algebraïsche topologie
  • Etalkohomologie
Label
Étale cohomology, J.S. Milne
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 313-320) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Étale morphisms -- Sheaf theory -- Cohomology -- The Brauer group -- The cohomology of curves and surfaces -- The fundamental theorems -- Appendix A. Limits -- Appendix B. Spectral sequences -- Appendix C. Hypercohomology
Control code
ocn948756256
Dimensions
unknown
Extent
1 online resource (xiii, 323 pages)
File format
unknown
Form of item
online
Isbn
9781400883981
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
10.1515/9781400883981
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt1bqrqvp
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)948756256
Label
Étale cohomology, J.S. Milne
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 313-320) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Étale morphisms -- Sheaf theory -- Cohomology -- The Brauer group -- The cohomology of curves and surfaces -- The fundamental theorems -- Appendix A. Limits -- Appendix B. Spectral sequences -- Appendix C. Hypercohomology
Control code
ocn948756256
Dimensions
unknown
Extent
1 online resource (xiii, 323 pages)
File format
unknown
Form of item
online
Isbn
9781400883981
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
10.1515/9781400883981
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt1bqrqvp
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)948756256

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