Trace forms of dyadic number fields (Q807662)

The trace form associated with a finite separable field extension K/k is the quadratic map \(x\to trace_{K/k} x^ 2\) defined on the k-vector space K. The appearance of trace forms in Witt classes of quadratic forms over algebraic number fields and local fields was studied by \textit{P. E. Conner} and \textit{R. Perlis} [A survey of trace forms of algebraic number fields (World Sci. 1984; Zbl 0551.10017)]. In this paper their results are complemented by an explicit characterization in terms of invariants of quadratic forms of those quadratic forms over the field \({\mathbb{Q}}_ 2\) of dyadic numbers which are isometric to trace forms of finite extensions \(K/{\mathbb{Q}}_ 2.\) \{P. E. Conner's name is misspelled throughout the paper.\}