Galois cohomology and class field theory. ([2020])

• Record Type: Book
• Uniform Title: Cohomologie galoisienne et théorie du corps de classes.
• Further Information: Note: David Harari.
• Authors: Harari, David
• Other Names: Yafaev, Andrei translator.
• 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.
• Publisher Details: [Les Ulis, France] Cham : EDP Sciences Springer
• Publication Date: 2020
• Copyright Date: 2020
• Extent: 1 online resource (xiv, 338 pages), illustrations
• Subjects: 514/.23; Galois cohomology; Class field theory; Number theory; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030439019; 3030439011
• Related ISBNs: 9783030439002; 3030439003
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from resource home page (ProQuest Ebook Central, viewed October 2, 2020).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.