Summary
Prasad and Rapinchuk asked if two quaternion divisionF-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.
2010 Mathematics subject classification. Primary: 16K20. Secondary: 11E04, 11E72.
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Garibaldi, S., Saltman, D.J. (2010). Quaternion Algebras with the Same Subfields. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_13
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DOI: https://doi.org/10.1007/978-1-4419-6211-9_13
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