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Submission: 2009, Jun 28

G. Prasad and A. Rapinchuk asked if two quaternion division F-algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F/K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields.

2000 Mathematics Subject Classification: primary 16K20; secondary 11E04, 12G05

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