Algebraic Groups and Number Theory: Volume 1

This revised second edition of the book provides a comprehensive treatment of the arithmetic theory of algebraic groups,including new material on groups with bounded generation and abstract arithmetic groups. It is suitable for self-study for graduate students and researchers in number theory,algebraic geometry,and related areas.

Format: Hardback
Length: 381 pages
Publication date: 07 September 2023
Publisher: Cambridge University Press

The first edition of this groundbreaking book offered a comprehensive and systematic exploration of the arithmetic theory of algebraic groups. In this revised and expanded second edition, published in two volumes, the same overarching goals are retained, while incorporating numerous corrections, enhancements, and a wealth of new material covering recent developments in the field. Volume I of this remarkable work begins with an extensive introduction to number theory, algebraic groups, and cohomology, encompassing both abelian and non-abelian aspects. It then delves into the study of algebraic groups over locally compact fields, providing a comprehensive treatment. The remaining two chapters offer a detailed exploration of arithmetic subgroups and reduction theory, covering both real and adelic settings.

In addition to its core content, Volume I includes valuable new material on groups with bounded generation and abstract arithmetic groups. This book is designed to cater to a diverse audience, including self-study graduate students eager to delve into the subject and researchers in number theory, algebraic geometry, and related fields seeking authoritative reference material.

With a clear and concise writing style, accompanied by comprehensive proofs whenever feasible, this book ensures accessibility to a wide range of readers. Its rigorous approach and comprehensive coverage make it an invaluable resource for anyone seeking to advance their knowledge in the field of algebraic groups and their arithmetic applications.

Weight: 648g
Dimension: 159 x 237 x 26 (mm)
ISBN-13: 9780521113618
Edition number: 2 Revised edition