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arXiv · 0906.5137

Quaternion algebras with the same subfields

Skip Garibaldi·David J. Saltman
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Abstract

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.

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Skip Garibaldi, David J. Saltman. 2009-06-28. Quaternion algebras with the same subfields. https://doi.org/10.1007/978-1-4419-6211-9_13

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