Generic Methods and Pfister Forms

It seems that any deeper investigation of the algebraic theory of quadratic forms requires a thorough knowledge of the theory of Pfister forms. They are the subject of this chapter. The investigation of Pfister forms is based essentially on the use of transcendental extensions of the ground field: One considers quadratic forms Σ a _ij X _i X _j . with indeterminates X _i . This approach leads naturally to the important concept of the function field of a quadratic form which is the function field of the quadratic Σ a _ij X _i X _j =0.