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A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology

by PierreGuillot (Author), Pierre Guillot (Author), Pierre Guillot (Author)

  • New

    Hardcover 2018

    $101.29
Synopsis

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker-Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.

$101.29

Quantity

20+ in stock

More Information

Format: Hardcover
 Pages: 306
 Publisher: Cambridge University Press
Published: 01 Nov 2018
ISBN 10: 1108421776
ISBN 13: 9781108421775

Media Reviews
Advance praise: 'This masterly written introductory course in number theory and Galois cohomology fills a gap in the literature. Readers will find a complete and nevertheless very accessible treatment of local class field theory and, along the way, comprehensive introductions to topics of independent interest such as Brauer groups or Galois cohomology. Pierre Guillot's book succeeds at presenting these topics in remarkable depth while avoiding the pitfalls of maximal generality. Undoubtedly a precious resource for students of Galois theory.' Olivier Wittenberg, Ecole normale superieure
Advance praise: 'Class field theory, and the ingredients of its proofs (e.g. Galois Cohomology and Brauer groups), are cornerstones of modern algebra and number theory. This excellent book provides a clear introduction, with a very thorough treatment of background material and an abundance of exercises. This is an exciting and indispensable book to anyone who works in this field.' David Zureick-Brown, Emory University, Georgia
Author Bio
Pierre Guillot is a lecturer at the Universite de Strasbourg and a researcher at the Institut de Recherche Mathematique Avancee (IRMA). He has authored numerous research papers in the areas of algebraic geometry, algebraic topology, quantum algebra, knot theory, combinatorics, the theory of Grothendieck's dessins d'enfants, and Galois cohomology.