Symmetric Bilinear Forms over Dedekind Rings and Global Fields

Abstract

Like the previous chapter this one deals with the number theoretic aspect of the theory of quadratic forms. Instead of the integers \( \mathbb{Z} \) and the rational field \( \mathbb{Q} \) we consider more generally an arbitrary algebraic number field and its ring of algebraic integers. Now and then we can be even more general by considering the quotient field of an arbitrary Dedekind domain. The theory of quadratic forms over algebraic number fields and the corresponding rings of integers is developed in detail in several books, especially O’Meara [1963] (to be referred to by OM). However, in the last few years several interesting results have been added to this theory. These new results, particularly those concerning the calculation of the Witt group are emphasized in this chapter.KeywordsSymmetric Bilinear FormGlobal FieldDiscrete Valuation RingDedekind DomainQuotient FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.