Displaying similar documents to “Graded quaternion symbol equivalence of function fields”

Graded Hilbert-symbol equivalence of number fields

Przemysław Koprowski (2015)

Discussiones Mathematicae - General Algebra and Applications

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We present a new criterion for the existence of Hilbert-symbol equivalence of two number fields. In principle, we show that the system of local conditions for this equivalence may be expressed in terms of Clifford invariants in place of Hilbert-symbols, shifting the focus from Brauer groups to Brauer-Wall groups.

Matching local Witt invariants

Przemysław Koprowski (2005)

Acta Mathematica Universitatis Ostraviensis

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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 generalisation. 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.