The Algebraic and Geometric Theory of Quadratic Forms

, by Elman, Richard; Karpenko, Nikita; Merkurjev, Alexander

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ISBN: 9780821843291 | 082184329X
Cover: Hardcover
Copyright: 8/15/2008

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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."--BOOK JACKET.

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Introduction
Classical theory of symmetric bilinear forms and quadratic forms: Bilinear forms Quadratic forms
Forms over rational function fields
function fields of quadrics
Bilinear and quadratic forms and algebraic extensions $u$-invariants
Applications of the Milnor conjecture On the norm residue homomorphism of degree two Algebraic cycles: Homology and cohomology
Chow groups Steenrod operations Category of Chow motives
Quadratic forms and algebraic cycles: Cycles on powers of quadrics
The Izhboldin dimension Application of Steenrod operations
The variety of maximal totally isotropic subspaces
Motives of quadrics
Appendices
Bibliography
Notation Terminology
Table of Contents provided by Publisher. All Rights Reserved.

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The Algebraic and Geometric Theory of Quadratic Forms

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