The Resource Galois cohomology and class field theory, David Harari
Galois cohomology and class field theory, David Harari
Resource Information
The item Galois cohomology and class field theory, David Harari represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 2 library branches.
Resource Information
The item Galois cohomology and class field theory, David Harari represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 2 library branches.
 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 PoitouTate 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 LubinTate 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 PoitouTate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet Lseries, 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
 Language

 eng
 fre
 eng
 Extent
 1 online resource (xiv, 338 pages)
 Contents

 Part I. Group cohomology and Galois cohomology: generalities. Cohomology of finite groups: basic properties
 Groups modified à la Tate, cohomology of cyclic groups
 Pgroups, the TateNakayama 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: LubinTate theory
 Part III. Global fields
 Basic facts about global fields
 Cohomology of the idèles: the class field axiom
 Reciprocity law and the BrauerHasseNoether theorem
 The abelianised absolute Galois group of a global field
 Part IV. Duality theorems. Class formations
 PoitouTate 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 lfunctions
 Complements on the Dirichlet density
 The first inequality
 Class field theory in terms of ideals
 Proof of the Čebotarev theorem
 Isbn
 9783030439019
 Label
 Galois cohomology and class field theory
 Title
 Galois cohomology and class field theory
 Statement of responsibility
 David Harari
 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 PoitouTate 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 LubinTate 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 PoitouTate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet Lseries, 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
 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
 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  Pgroups, the TateNakayama 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: LubinTate theory  Part III. Global fields  Basic facts about global fields  Cohomology of the idèles: the class field axiom  Reciprocity law and the BrauerHasseNoether theorem  The abelianised absolute Galois group of a global field  Part IV. Duality theorems. Class formations  PoitouTate 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 lfunctions  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
 10.1007/978303043
 Other physical details
 illustrations.
 Specific material designation
 remote
 System control number
 (OCoLC)1163554954
 Label
 Galois cohomology and class field theory, David Harari
 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  Pgroups, the TateNakayama 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: LubinTate theory  Part III. Global fields  Basic facts about global fields  Cohomology of the idèles: the class field axiom  Reciprocity law and the BrauerHasseNoether theorem  The abelianised absolute Galois group of a global field  Part IV. Duality theorems. Class formations  PoitouTate 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 lfunctions  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
 10.1007/978303043
 Other physical details
 illustrations.
 Specific material designation
 remote
 System control number
 (OCoLC)1163554954
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/GaloiscohomologyandclassfieldtheoryDavid/ecSogHKDOjs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/GaloiscohomologyandclassfieldtheoryDavid/ecSogHKDOjs/">Galois cohomology and class field theory, David Harari</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>