Quadratic Forms

✍ Scribed by Winfried Scharlau

• Publisher: Queen's University
• Year: 1970
• Tongue: English
• Leaves: 167
• Series: Queen's Papers in Pure and Applied Mathematics 22
• Category: Library

✦ Table of Contents

Preface
Table of Contents
Chapter 1. The Theory of Witt
1.1. Bilinear forms and quadratic forms
1.2 Quadratic forms for charateristics not 2
1.3 Direct sum and orthogonal decomposition
1.4 Hyperbolic planes
1.5 Witt's Theorem. Witt decomposition.
1.6. The Grothendieck ring and the Witt ring
Appendix to Chapter 1.
Chapter 2. The Theory of Pfister
2.1 Multiplicative forms and applications to the structure of the Witt ring.
2.2 The method of transfer
2.3 Pfister's Local-Global Principle
2.4 Representation of definite functions as sums of squares
2.5 The theorems of Cassels. Fields of prescribed level.
Appendix to Chapter 2
Chapter 3. Simple Algebras and Clifford Algebras
3.1 Wedderburn Theory
3.2 The Brauer Group
3.3 Clifford alrebras
3.4 Quaternion algebras
3.5. The graded Brauer group. The Witt invariant and the Hasse invariant.
3.6. The Spin group and the Spinor norm
Appendix to Chapter 3.
Chapter 4. Classification Theory
4.1 Resumé and general results
4.2 Quadratic forms over local fields
4.3 Fields with only one non-trivial quaternion algebra
4.4 Results from global class field theory
4.5 Quadratic forms over global fields. The Hasse-Minkowski theorem.
Appendix to Chapter 4
Appendix. Quadratic Forms and Galois Cohomology
Bibliography