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Algebraic Groups and Their Birational Invariants

V. E. Voskresenskiĭ Samara State University, Samara, Russia
Available Formats:
Electronic ISBN: 978-1-4704-1622-5
Product Code: MMONO/179.S.E
List Price: $79.00 MAA Member Price:$71.10
AMS Member Price: $63.20 Click above image for expanded view Algebraic Groups and Their Birational Invariants V. E. Voskresenskiĭ Samara State University, Samara, Russia Available Formats:  Electronic ISBN: 978-1-4704-1622-5 Product Code: MMONO/179.S.E  List Price:$79.00 MAA Member Price: $71.10 AMS Member Price:$63.20
• Book Details

Translations of Mathematical Monographs
Volume: 1791998; 218 pp
MSC: Primary 20; Secondary 14;

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.

• Chapters
• 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
• Reviews

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

Mathematical Reviews
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• Get Permissions
Volume: 1791998; 218 pp
MSC: Primary 20; Secondary 14;

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.

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

Mathematical Reviews
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