Coverart for item
The Resource Galois cohomology and class field theory, David Harari

Galois cohomology and class field theory, David Harari

Label
Galois cohomology and class field theory
Title
Galois cohomology and class field theory
Statement of responsibility
David Harari
Creator
Contributor
Author
Translator
Subject
Language
  • eng
  • fre
  • eng
Summary
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference"--Publisher's description
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorName
Harari, David
Dewey number
514/.23
Index
index present
LC call number
QA612.3
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Yafaev, Andrei
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Galois cohomology
  • Class field theory
  • Number theory
Label
Galois cohomology and class field theory, David Harari
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Part I. Group cohomology and Galois cohomology: generalities. Cohomology of finite groups: basic properties -- Groups modified à la Tate, cohomology of cyclic groups -- P-groups, the Tate-Nakayama theorem -- Cohomology of profinite groups -- Cohomological dimension -- First notions of Galois cohomology -- Part II. Local fields. Basic facts about local fields -- Brauer group of a local field -- Local class field theory: the reciprocity map -- The Tate local duality theorem -- Local class field theory: Lubin-Tate theory -- Part III. Global fields -- Basic facts about global fields -- Cohomology of the idèles: the class field axiom -- Reciprocity law and the Brauer-Hasse-Noether theorem -- The abelianised absolute Galois group of a global field -- Part IV. Duality theorems. Class formations -- Poitou-Tate duality -- Some applications -- Appendices. Some results from homological algebra. Generalities on categories -- Functors -- Abelian categories -- Categories of modules -- Derived functors -- Ext and tor -- Spectral sequences -- A survey of analytic methods -- Dirichlet series -- Dedekind [zeta] function; Dirichlet l-functions -- Complements on the Dirichlet density -- The first inequality -- Class field theory in terms of ideals -- Proof of the Čebotarev theorem
Control code
1163554954
Extent
1 online resource (xiv, 338 pages)
Form of item
online
Isbn
9783030439019
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-030-43
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)1163554954
Label
Galois cohomology and class field theory, David Harari
Publication
Copyright
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Part I. Group cohomology and Galois cohomology: generalities. Cohomology of finite groups: basic properties -- Groups modified à la Tate, cohomology of cyclic groups -- P-groups, the Tate-Nakayama theorem -- Cohomology of profinite groups -- Cohomological dimension -- First notions of Galois cohomology -- Part II. Local fields. Basic facts about local fields -- Brauer group of a local field -- Local class field theory: the reciprocity map -- The Tate local duality theorem -- Local class field theory: Lubin-Tate theory -- Part III. Global fields -- Basic facts about global fields -- Cohomology of the idèles: the class field axiom -- Reciprocity law and the Brauer-Hasse-Noether theorem -- The abelianised absolute Galois group of a global field -- Part IV. Duality theorems. Class formations -- Poitou-Tate duality -- Some applications -- Appendices. Some results from homological algebra. Generalities on categories -- Functors -- Abelian categories -- Categories of modules -- Derived functors -- Ext and tor -- Spectral sequences -- A survey of analytic methods -- Dirichlet series -- Dedekind [zeta] function; Dirichlet l-functions -- Complements on the Dirichlet density -- The first inequality -- Class field theory in terms of ideals -- Proof of the Čebotarev theorem
Control code
1163554954
Extent
1 online resource (xiv, 338 pages)
Form of item
online
Isbn
9783030439019
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-030-43
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)1163554954

Library Locations

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      38.944377 -92.326537
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