Abstract
If (A,σ) is a central simple algebra of even degree with orthogonal involution, then for the map of Galois cohomology sets fromH 1(F,SO(A,σ)) to the 2-torsion in the Brauer group ofF, we describe fully the image of a given element ofH 1(F,SO(A,σ)) and prove that this description is correct in two different ways. As an easy consequence, we derive a result of Bartels [Bar, Satz 3].
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Supported in part by the National Fund for Scientific Research (Belgium).
Supported in part by the NSF.
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