ABSTRACT
In this chapter we discuss invariants of quadratic forms expressed in terms of similarity classes of quaternion algebras. The Hasse invariant is an invariant of equivalence relation and the Witt invariant is an invariant of similarity relation. The two invariants are related to each other in a way resembling the relation between determinant and discriminant of a quadratic form. We discuss some applications of the invariants to classification of quadratic forms. As a consequence of the existence of Witt invariant we will prove the Arason-Pfister‘s Hauptsatz for the third power of the fundamental ideal of the Witt ring. As an application we prove Harrison’s criterion for Witt equivalence of fields. This completes the project begun in Chapter 20.
