Galois cohomology and class field theory

Galois cohomology and class field theory / David Harari.

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 a...

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Bibliographic Details
Main Author: Harari, David (Author)
Other Authors: Yafaev, Andrei (Translator)
Format: eBook
Language:English
French
Published: [Les Ulis, France] : Cham : EDP Sciences ; Springer., [2020]
Series:Universitext.
Subjects:
Galois cohomology.
Class field theory.
Number theory.
Mathematics > Number Theory.
Galois cohomology
Class field theory
Number theory
Online Access:Click for online access
Uniform Title:Cohomologie galoisienne et théorie du corps de classes.
Table of 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.

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