Geodesic
Graded quaternion symbol equivalence of function fields
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1311-1319 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.
We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.
Classification : 11E10, 11E81, 14H05, 14P05, 16K50
Keywords: Brauer group; Brauer-Wall group; Witt equivalence 
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Koprowski, Przemysław. Graded quaternion symbol equivalence of function fields. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1311-1319. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a12/

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