Local-global principles for Witt rings
For a collection \({\mathbf K}\) of algebraic extensions of a field \(K\) there is the natural homomorphism of the Witt ring \(W(K)\) into the sheaf product of the Witt rings of fields in \({\mathbf K}\). Conditions are studied under which the homomorphism turns out to be surjective or bijective. If the fields in \({\mathbf K}\) are contained in the quadratic closure of \(K\) and if the collection \({\mathbf K}\) is closed in a certain sense, then the natural homomorphism is an isomorphism if and only if the Galois group of the quadratic closure of \(K\) over \(K\) is a free pro-2 product of the Galois groups of the quadratic closure of \(K\) over the fields in the collection \({\mathbf K}\). This is applied to a computation of the Witt rings of real-projective fields.
computation of Witt rings of real-projective fields
scientific article; zbMATH DE number 500591
scientific article