Quadratic Forms with Applications to Algebraic Geometry and Topology

ISBN-13: 9780521467551 / Angielski / Miękka / 1995 / 188 str.

Albrecht Pfister; J. W. S. Cassels; N. J. Hitchin

Opis

This volume discusses results about quadratic forms that give rise to interconnections among number theory, algebra, algebraic geometry, and topology. The author deals with various topics including 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 has made this book as self-contained as possible. This book brings together thirty years' worth of results certain to interest anyone whose research touches on quadratic forms.

Recenzje

'A very readable complement to the standard treatments.' Mathematica

Spis treści

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.