Matching local Witt invariants. (English) Zbl 1251.11023

Summary: The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence – once it is expressed in terms of the Witt invariant – admits a natural generalization. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.


11E81 Algebraic theory of quadratic forms; Witt groups and rings
11E10 Forms over real fields
14H05 Algebraic functions and function fields in algebraic geometry
14P05 Real algebraic sets
16K50 Brauer groups (algebraic aspects)
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