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Quadratic forms over totally p-adic fields. (Spanish) Zbl 0574.10027

Proc. XIIth annu. Meet. Spanish mathematicians, Málaga 1976, 25-32 (1983).
[For the entire collection see Zbl 0535.00006.]
Let K be a field of numbers and \(P\neq \emptyset\) a finite set of prime elements of K. Then the totally P-adic field \(K_ P\) over K is formed by all finite extensions of K with the property that the elements of P decompose completely. The paper gives a characterization of the different quadratic forms over \(K_ P\) and investigates the Witt ring \(W(K_ P)\) of \(K_ P\). It turns out that \(W(K_ P)\) is infinite. The additive group of \(W(K_ P)\) is described by means of the Clifford invariant.
Reviewer: W.B.Müller

MSC:

11E08 Quadratic forms over local rings and fields
11E16 General binary quadratic forms

Citations:

Zbl 0535.00006