ISBN 9780821868768,Algebraic And Geometric Theory Of Quadratic

Algebraic And Geometric Theory Of Quadratic

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American Mathematical Society

Publication Year 2011

ISBN 9780821868768

ISBN-10 0821868764


Number of Pages 448 Pages
Language (English)

Educational: Mathematics & numeracy

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.