Translations of Mathematical Monographs 1998; 218 pp; softcover Volume: 179 ISBN10: 0821872885 ISBN13: 9780821872888 List Price: US$75 Member Price: US$60 Order Code: MMONO/179.S
 Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This bookwhich can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, \(R\)equivalence, projective toric varieties, invariants of finite transformation groups, and indexformulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading. Readership Graduate students and research mathematicians working in algebraic geometry, algebraic groups and related fields. Reviews "This book is remarkably complete, concise and essentially selfcontained."  Mathematical Reviews Table of Contents  Forms and Galois cohomology
 Birational geometry of algebraic tori
 Invariants of finite transformation groups
 Arithmetic of linear algebraic groups
 Tamagawa numbers
 \(R\)equivalence in algebraic groups
 Index formulas in arithmetic of algebraic tori
 Bibliographical remarks
 Bibliography
