Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series)

Pfister, Albrecht

Cambridge University Press（1995/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 188 p.
• 言語 ENG
• 商品コード 9780521467551
• DDC分類 512.74

Full Description

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.

Contents

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.