Quaternion algebras with the same subfields

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.

References in corpus (2)

• Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
• Wild Pfister forms over Henselian fields, K-theory, and conic division algebras

Cited by in corpus (9)

• Simple groups stabilizing polynomials
• Open Problems on Central Simple Algebras
• Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces
• Division Algebras With Infinite Genus
• Counting and effective rigidity in algebra and geometry
• Division algebras with the same maximal subfields
• Geometric spectra and commensurability
• On division algebras having the same maximal subfields
• Noether's problem and rationality problem for multiplicative invariant fields: a survey