Quadratic forms with applications to algebraic geometry and topology
著者
書誌事項
Quadratic forms with applications to algebraic geometry and topology
（London Mathematical Society lecture note series, 217）
Cambridge University Press, 1995
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This volume has grown out of lectures given by Professor Pfister over many years. The emphasis here is placed on results about quadratic forms that give rise to interconnections between number theory, algebra, algebraic geometry and topology. Topics discussed include Hilbert's 17th problem, the Tsen-Lang theory of quasi algebraically closed fields, the level of topological spaces and systems of quadratic forms over arbitrary fields. Whenever possible proofs are short and elegant, and the author's aim was to make this book as self-contained as possible. This is a gem of a book bringing together thirty years' worth of results that are certain to interest anyone whose research touches on quadratic forms.
目次
- 1. The representation theory of Cassels
- 2. Multiplicative quadratic forms
- 3. The level of fields, rings and topological spaces
- 4. Hilbert's homogeneous nullstellensatz
- 5. Tsen-Lang theory
- 6. Hilbert's 17th problem
- 7. The Pythagoras number
- 8. The u-invariant
- 9. Systems of quadratic forms
- 10. The level of projective spaces.
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