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The Algebraic and Geometric Theory of Quadratic Forms
Richard Elman, University of California, Los Angeles, CA, Nikita Karpenko, Université Pierre et Marie Curie - Paris 6, France, and Alexander Merkurjev, University of California, Los Angeles, CA
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Colloquium Publications
2008; 435 pp; hardcover
Volume: 56
ISBN-10: 0-8218-4329-X
ISBN-13: 978-0-8218-4329-1
List Price: US$81 Member Price: US$64.80
Order Code: COLL/56

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This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given.

Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Graduate students and research mathematicians interested in algebraic geometry and number theory.

Reviews

"This book is a welcome addition to the vast literature on quadratic forms, summarizing recent advances of the theory, highlighting the algebraic geometry approach and shedding new light on the classical results."

-- MAA Reviews

"Overall, this book is an outstanding achievement and will be an indispensable reference for specialists, though challenging for beginners."

-- Mathematical Reviews

"The first part of the book may well serve as a modern introduction to the classical algebraic theory of quadratic forms ... the exposition is throughout lucid, detailed, enlightening and inspiring, very much to the benefit of the keen reader. No doubt, the authors have done an admirable and rewarding job by making such a modern, encyclopedic text available to the mathematical community as a whole."

-- Zentralblatt MATH