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

Pierre Guillot

ISBN 10: 1108432247 / ISBN 13: 9781108432245

Published by Cambridge University Press, 2018

About this Item

2018. 1st Edition. Paperback. . . . . . Books ship from the US and Ireland.

Seller Inventory # V9781108432245

Bibliographic Details

• Title: A Gentle Course in Local Class Field Theory: Local Number Fields, Brauer Groups, Galois Cohomology
• Publisher: Cambridge University Press
• Publication Date: 2018
• Language: English
• ISBN 10: 1108432247
• ISBN 13: 9781108432245
• Binding: Soft cover
• Condition: New

About this title

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 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.