Quaternion algebras with the same subfields

Details Quaternion algebras with the same subfields Quaternion algebras with the same subfields

2009-06-28

arxiv.org/abs/0906.5137v1

pages 225-238 in the book "Quadratic forms, linear algebraic groups, and cohomology", Springer, 2010

Mathematics

Rings and Algebras

Scientific paper

10.1007/978-1-4419-6211-9_13

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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