Canonical localizers and nonmaximal orders in the Witt setting (Q798696)

Canonical localizers relating the number field trace to the residue field trace arise in the study of the Witt group, and in the study of the knot concordance group. These are required to do computations in the Witt setting when nonmaximal orders in an algebraic number field are studied. This paper gives criteria under which these canonical localizers can be computed, and analyzes the problems which occur in using the boundary exact sequence. It also gives an example of an element of order 4 in the knot concordance group \(C_ S({\mathbb{Z}})\), where \(S={\mathbb{Z}}(\theta)\) is a nonmaximal order in the algebraic number field \({\mathbb{Q}}(\theta)\).