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Algebraic Groups and Their Birational Invariants
V. E. Voskresenskiĭ, Samara State University, Russia

Translations of Mathematical Monographs
1998; 218 pp; softcover
Volume: 179
ISBN-10: 0-8218-7288-5
ISBN-13: 978-0-8218-7288-8
List Price: US$79
Member Price: US$63.20
Order Code: MMONO/179.S
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Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which 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 index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.


Graduate students and research mathematicians working in algebraic geometry, algebraic groups and related fields.


"This book is remarkably complete, concise and essentially self-contained."

-- 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
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