A Gentle Course in Local Class Field Theory

Local Number Fields, Brauer Groups, Galois Cohomology

Pierre Guillot (Autor)

Buch | Softcover

306 Seiten

2018
Cambridge University Press (Verlag)
978-1-108-43224-5 (ISBN)

Artikel merken

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.

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.

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.

Part I. Preliminaries: 1. Kummer theory; 2. Local number fields; 3. Tools from topology; 4. The multiplicative structure of local number fields; Part II. Brauer Groups: 5. Skewfields, algebras, and modules; 6. Central simple algebras; 7. Combinatorial constructions; 8. The Brauer group of a local number field; Part III. Galois Cohomology: 9. Ext and Tor; 10. Group cohomology; 11. Hilbert 90; 12. Finer structure; Part IV. Class Field Theory: 13. Local class field theory; 14. An introduction to number fields.

Erscheinungsdatum	06.12.2018
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	174 x 247 mm
Gewicht	530 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-108-43224-7 / 1108432247
ISBN-13	978-1-108-43224-5 / 9781108432245
Zustand	Neuware