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 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
- 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
- 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
- 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 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
- 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 -- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Galois-cohomology-and-class-field-theory-David/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/Galois-cohomology-and-class-field-theory-David/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>
