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
Keywords and Phrases:
Full text: dvi.gz 29 k, dvi 62 k, ps.gz 569 k, pdf.gz 152 k, pdf 170 k.