Local-global principles for witt rings

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Abstract

This paper investigates the connection between the Witt and Witt-Grothendieck rings of a field K and the corresponding rings of a given collection K of separable algebraic extensions of K. In particular, it deals with the question whether the former rings are the "sheaf products" of the latter rings. If K consists of pro-2 extensions and is closed in the natural topology then this happens precisely when the 2-Galois group of K is the free pro-2 product of the 2-Galois groups of the fields in K. This result is used to classify the quadratic forms over the field of totally real numbers, and more generally, over real-projective fields.

Original languageEnglish
Pages (from-to)153-166
Number of pages14
JournalJournal of Pure and Applied Algebra
Volume90
Issue number2
DOIs
StatePublished - 1 Dec 1993
Externally publishedYes

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