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

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.

About the Author

Pierre Guillot is a lecturer at the Université de Strasbourg and a researcher at the Institut de Recherche Mathématique Avancée (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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2018
• ISBN 10: 1108432247
• ISBN 13: 9781108432245
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 306