The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Author: Vladimir Platonov, Andrei Rapinchuk, Igor Rapinchuk
Binding Type: Hardcover
Publisher: Cambridge University Press
Published: 11/02/2023
Series: Cambridge Studies in Advanced Mathematics #205
Pages: 381
Weight: 1.35lbs
Size: 9.06h x 5.91w x 0.94d
ISBN: 9780521113618
2nd Edition