Witt equivalence of global fields. II. Relative quadratic extensions

Abstract

This paper explores the consequences of the Hasse Principle for Witt equivalence of global fields in the case of relative quadratic extensions. We are primarily interested in generating the Witt equivalence classes of quadratic extensions of a given number field, and we study the structure of the class, the number of classes, and the structure of the set of classes. Along the way, we reprove several results obtained earlier in the absolute case of the rational ground field, giving unified and short proofs based on the Hasse Principle.