Quaternion algebras with the same subfields
Rings and Algebras
2010-12-15 v1
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.
Cite
@article{arxiv.0906.5137,
title = {Quaternion algebras with the same subfields},
author = {Skip Garibaldi and David J. Saltman},
journal= {arXiv preprint arXiv:0906.5137},
year = {2010}
}