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On the Milnor exact sequence for rational quadratic forms. (English) Zbl 0933.11022

Győry, Kálmán (ed.) et al., Number theory in progress. Proceedings of the international conference organized by the Stefan Banach International Mathematical Center in honor of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, June 30–July 9, 1997. Volume 1: Diophantine problems and polynomials. Berlin: de Gruyter. 531-537 (1999).
The structure of the Witt group of the rational numbers \(\mathbb{Q}\) is given by the exactness of the Milnor sequence for the Witt group of the field \(\mathbb{Q}\). This is a standard result in quadratic form theory, and the usual proof of exactness of this sequence is based on Milnor’s approach. In this paper the author provides a new proof based on purely quadratic form theoretical results, in particular quadratic form theory over the \(p\)-adic fields \(\mathbb{Q}_p\) and the strong Hasse principle for isotropy of rational quadratic forms.
For the entire collection see [Zbl 0911.00025].

MSC:

11E81 Algebraic theory of quadratic forms; Witt groups and rings
11E70 \(K\)-theory of quadratic and Hermitian forms
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