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

Guillot, Pierre

Softcover

ISBN 10: 1108432247 ISBN 13: 9781108432245

Publisher: Cambridge University Press, 2018

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.

About this title

Review

'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, École normale supérieure

'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

Book Description

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. Written for beginning graduate students and advanced undergraduates, the material will find use across disciplines including number theory, representation theory, algebraic geometry, and algebraic topology.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2018
• ISBN 10: 1108432247
• ISBN 13: 9781108432245
• Binding: Paperback
• Language: English
• Number of pages: 306