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Galois cohomology and class field theory / David Harari.

By: Harari, David [author.].
Contributor(s): Yafaev, Andrei [translator.].
Material type: TextTextSeries: Universitext: Publisher: [Les Ulis, France] : Cham : EDP Sciences ; Springer., [2020]Copyright date: ©2020Description: xiv, 338 pages : E 24.99 illustrations. 24 cms.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030439002 (pbk.); 3030439011.Uniform titles: Cohomologie galoisienne et théorie du corps de classes. English Subject(s): Galois cohomology | Class field theory | Number theoryGenre/Form: Electronic books. | Electronic books.DDC classification: 514/.23
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.
List(s) this item appears in: 2021-07-26
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		514.23 HAR (Browse shelf) Checked out 04/04/2024 10874
Total holds: 0

Includes bibliographical references and index.

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.

Description based on online resource; title from resource home page (ProQuest Ebook Central, viewed October 2, 2020).